Answers
Given:
Find-:
The value of "x."
Explanation-:
Use a trigonometric is:
[tex]\tan\theta=\frac{Perpendicular}{\text{ Base}}[/tex]In a triangle:
[tex]\begin{gathered} \text{ Angle}=x \\ \\ \text{ Base }=3 \\ \\ \text{ Pespendicular }=4 \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan x=\frac{4}{3} \\ \\ x=\tan^{-1}(\frac{4}{3}) \\ \\ x=53.13 \end{gathered}[/tex]So, the angle is 53 degree
Related Questions
Give Line SV parallels Line TU and Triangle SVX =~ Triangle UTXProve: VUTS is a parallelogramWrite a Paragraph Proof.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the proof are as follows:
Since
[tex]\begin{gathered} \bar{SV}\text{ is parallel to} \\ \bar{TU} \end{gathered}[/tex]and
[tex]\text{Triangle SVX }\cong\text{ Triangle UTX}[/tex]Then,
[tex]VX\cong\text{ XT ( by }CPCTC\text{ ) }[/tex]CPCTC means corresponding parts of congruent triangles are congruent
and
[tex]UX\text{ }\cong XS\text{ ( by CPCTC)}[/tex]Thus,
VUTS is a parallelogram since diagonals of a parallelogram bisect each other
The arcade charges $125.00 to reserve the location, and then $15.00 per person. Which expressionrepresents the total cost for any number of people n?
Answers
Let 'n' represent the number of people. Sin the arcade charces 15 per person, then we have the following first term:
[tex]15n[/tex]since the charge to reserve is $125, we have:
[tex]15n+125[/tex]thus, if 'c' represents the total cost, then the expression to represent this situation is:
[tex]c=15n+125[/tex]Please help me!!!!!!!
Answers
Answer:
B. (19/24)
Step-by-step explanation:
1 1 5
------ + ------ + -------
4 8 12
1(6) 1(3) 5(2)
------ + ------ + -------
4(6) 8(3) 12(2)
6 3 10 19
------ + ------ + ------- = -------
24 24 24 24
I hope this helps!
identify the reflection of the figure with vertices P (2, -12), Q (-3, 13), and R (-5, - 15) across the x-axis.
Answers
EXPLANATION:
We are given the following coordinates for a figure on the coordinate plane;
[tex]\begin{gathered} P(2,-12) \\ Q(-3,13) \\ R(-5,-15) \end{gathered}[/tex]To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.
Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.
Therefore, for the vertices given, the reflection across the x-axis would be;
[tex]P(2,-12)\rightarrow P^{\prime}(2,12)[/tex][tex]Q(-3,13)\rightarrow Q^{\prime}(-3,-13)[/tex][tex]R(-5,-15)\rightarrow R^{\prime}(-5,15)[/tex]ANSWER:
The coordinates of the reflection across the x-axis therefore will be;
[tex]\begin{gathered} P^{\prime}(2,12) \\ Q^{\prime}(-3,-13) \\ R^{\prime}(-5,15) \end{gathered}[/tex]Pl3ase help me with Geometry. right angles and perpendicular angles
Answers
(Question 3)
Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that
[tex]\bar{DB}=\bar{BE}[/tex]Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,
[tex]\begin{gathered} 3x-9=x+21\rightarrow3x-x=21+9\rightarrow2x=30 \\ \rightarrow x=\frac{30}{2} \\ \rightarrow x=15 \end{gathered}[/tex]We know that
[tex]AE=x+21[/tex]We'll just have to plug in the value of x we calculated to find the lenght of AE
[tex]AE=15+21\rightarrow AE=36[/tex]Therefore, AE = 36
(Question 4)
Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that
Therefore, RS = 5
Complete the synthetic division work below to divide 5x^3 - 3x^2 + 2x - 1 by x+1 Fill in the blank with the four numbers that would go below the line. Separate numbers by commas. 5 -3 2 - 1
Answers
Abraham, this is the solution of the polynomials division:
5x^3 - 3x^2 + 2x - 1/ x+1
Step 1:
5x² + (-8x² + 2x - 1)/(x + 1)
Step 2:
5x² - 8x + (10x - 1)/(x + 1)
Step 3:
5x² -8x + 10 + (-11/x + 1)
The four numbers below the line are: 5 -8 10 - 11
the answer and how to figure questions out like this!
Answers
In order to find the exponential regression we are going to select some values of the given data.
STEP 1An special value is when x=0.
On the table we can see that when x=0 then y=9
Replacing x by 0 in the given choices, we have that:
[tex]\begin{gathered} A\text{.} \\ y=8.04\cdot0.98^x \\ \downarrow \\ y=8.04\cdot0.98^0=8.04\cdot1 \\ =8.04 \end{gathered}[/tex][tex]\begin{gathered} B\text{.} \\ y=3.02\cdot3.67^x \\ \downarrow \\ y=3.02\cdot3.67^0=3.02\cdot1 \\ =3.02 \end{gathered}[/tex][tex]\begin{gathered} C\text{.} \\ y=6.61\cdot1.55^x \\ \downarrow \\ y=6.61\cdot1.55^0=6.61\cdot1 \\ =6.61 \end{gathered}[/tex][tex]\begin{gathered} D\text{.} \\ y=2.27\cdot2.09^x \\ \downarrow \\ y=2.27\cdot2.09^0=2.27\cdot1 \\ =2.27 \end{gathered}[/tex]Observing the results we have that the two choices with closer results to 9 are A (with 8.04) and C (with 6.61)
STEP 2Now, we are going to select two additional values from the table in order to find which is the best answer: A or C.
Let's take x=1.
When x = 1, then y=10.
Replacing on the equation A we have:
[tex]\begin{gathered} A\text{.} \\ y=8.04\cdot0.98^x \\ \downarrow \\ y=8.04\cdot0.98^1=8.04\cdot0.98 \\ =7.879 \end{gathered}[/tex]and for the equation C:
[tex]\begin{gathered} C\text{.} \\ y=6.61\cdot1.55^x \\ \downarrow \\ y=6.61\cdot1.55^1=6.61\cdot1.55 \\ =10.2455 \end{gathered}[/tex]For x=1, the nearest result is from the equation C.
Let's verify what happens when x=2.
When x=2 then y=16. Replacing on the equation A we have:
[tex]\begin{gathered} A\text{.} \\ y=8.04\cdot0.98^x \\ \downarrow \\ y=8.04\cdot0.98^2 \\ =7.7216 \end{gathered}[/tex]and for the equation C:
[tex]\begin{gathered} C\text{.} \\ y=6.61\cdot1.55^x \\ \downarrow \\ y=6.61\cdot1.55^2 \\ =15.88 \end{gathered}[/tex]Again, for x=2, the nearest result is from the equation C.
Then, we can conclude that the best candidate is equation C.
We could try other values of x to double check:
[tex]\begin{gathered} C\text{.} \\ y=6.61\cdot1.55^x \\ \downarrow \\ y=6.61\cdot1.55^2 \\ =15.88 \end{gathered}[/tex]The graph of f(x) = StartRoot x EndRoot is reflected across the y-axis to create the graph of function g. How do the domains of f and g compare?The domains of f and g are both x ≥ 0.The domains of f and g are both all real numbers.The domain of f is x ≥ 0, while the domain of g is x ≤ 0.The domain of f is x ≤ 0, while the domain of g is x ≥ 0.
Answers
Step-by-step explanation:
Given that f(x) is reflected across the y-axis to create the graph of function g.
i.e. f is reflected on the line x=0
Hence x will become -x in g.
When domain of f is x>=0 the domain of g can only be x less than or equal to 0.
Hence answer is option 3,The domain of f is x ≥ 0, while the domain of g is x ≤ 0
Answer:
The third one
Step-by-step explanation:
Internet rates for two companies are shown in the table. After how many months of service is the total cost thesame no matter which company is used? What is this total cost?Intemet Service ProviderChargesTyson's Ethernet $100 activation fee plus $20 per monthDarriana's DSL$30 per month
Answers
We need to find in which month we have that the total cost is the same, so we are going to do the equations of cost of the two companies
For the Tyson's Ethernet we have that the equation is
[tex]f(m)=20\cdot m+100[/tex]with m the month. And for the Darriana's DSL the equation is
[tex]g(m)=30\cdot m[/tex]We need to equalize the equations, so we have
[tex]\begin{gathered} 30m=20m+100 \\ 30m-20m=20m+100-20m \\ 10m=100 \\ m=\frac{100}{10}=10 \end{gathered}[/tex]Now to see the cost we replace in the two equations( wiith this we also verify), we have that
[tex]\begin{gathered} f(10)=20\cdot10+100=200+100=300 \\ g(10)=30\cdot10=300 \end{gathered}[/tex]The answer is: after 10 months the total cost is the same, and this cost is $300.
if andrew can run 60 meters in 6 seconds, how many meters can he run in 1 second?
Answers
Explanation
Step 1
the sp
The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w
Answers
Step 1
Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?
Step 2
[tex]\begin{gathered} l=\frac{a}{w} \\ l=\frac{6x^2y+4y^2x}{2xy} \end{gathered}[/tex][tex]\begin{gathered} factorize \\ l=\frac{2xy\left(3x+2y\right)}{2xy} \end{gathered}[/tex]Thus;
[tex]l=3x+2y[/tex]Answer;
[tex]l=3x+2y[/tex]I need help with this problem.It say solve the following inequalities and graph it on the Number Line.
Answers
Given the inequality:
[tex]13>-4x-7[/tex]• You can solve it as follows:
1. Apply the Addition Property of Inequality by adding 7 to both sides of the inequality:
[tex]13+(7)>-4x-7+(7)[/tex][tex]20>-4x[/tex]2. Apply the Division Property of Inequality by dividing both sides of the inequality by -4 (since you are dividing both sides by a negative number, the direction of the inequality symbol changes):
[tex]\begin{gathered} \frac{20}{-4}<\frac{x}{-4} \\ \\ -53. You can rewrite the solution in this form:[tex]x>-5[/tex]• In order to graph the solution on the Number Line, you can follow these steps:
1. Since the symbol is:
[tex]>[/tex]You need to draw an open circle over the number -5.
2. Draw a line from the circle to the right.
Then, you get:
Hence, the answer is:
• Solution:
[tex]x>-5[/tex]• Number Line:
Select the following sentence that represents the equation below:
3(n2+1)=3n+12
Responses
The sum of the product of two and a number plus one times three is equal to twelve more than the product of three and the same number.
The sum of the product of two and a number plus one times three is equal to twelve more than the product of three and the same number., EndFragment,
Three times the sum of twice a number and one is equal to twelve less than the product of three and the same number.
Three times the sum of twice a number and one is equal to twelve less than the product of three and the same number., EndFragment,
The quotient of a number and two increased by one is equal to twelve more than the quotient of three and the same number.
The quotient of a number and two increased by one is equal to twelve more than the quotient of three and the same number., EndFragment,
Three times the sum of a number divided by two and one is equal to three times the same number increased by twelv
Answers
The answer is, Three times the sum of twice a number and one is equal to twelve less than the product of three and the same number.
Three times the sum of twice a number and one is equal to twelve less than the product of three and the same number.
What is a quotient?It has a wide spread throughout the Mathematics. It is referred to as the integer part of a division, or as the fraction, or as a ratio. It is used when indicating the presence or the degree of a characteristic in something or by someone. Quotient is the result of a division. It is obtained when we divide one number by another. Quotient means how many times. And it is derived from the Latin.
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Question #2Several points are plotted on the graph. Which of the plotted points on the graph represent the zeros of the function:f (x) = (x^2+ 2x- 8) (x – 6)
Answers
Given function is:
[tex]f(x)=(x^2+2x-8)(x-6)[/tex]Now put f(x)=0
[tex]\begin{gathered} (x^2+2x-8)(x-6)=0 \\ (x^2+2x-8)=0,(x-6)=0 \\ x-6=0 \\ x=6 \end{gathered}[/tex]so the first point is (6,0) now for another points:
[tex]\begin{gathered} (x^2+2x-8)=0 \\ (x^2+4x-2x-8)=0 \\ x(x+4)-2(x+4)=0 \\ (x+4)(x-2)=0 \\ x=-4,2 \end{gathered}[/tex]So the points are (-4,0) and (2,0) and(6,0)
Hence the correct options are 1,2 and 4.
If F(x) =8+11 X-3X², finda. What is F (5)? b. What is F (x + b)?c. What is F (-3)?
Answers
a. Solve for F(5).
To solve for F(5), substitute x = 5 to the given function, and evaluate accordingly to the operation
[tex]\begin{gathered} F(x)=8+11x-3x^2 \\ F(5)=8+11(5)-3(5)^2 \\ F(5)=8+55-3(25) \\ F(5)=63-75 \\ F(5)=-12 \end{gathered}[/tex]b. Solve for F(x+b)
Again we substitute the paremeters by x+b to the given function, and we get
[tex]\begin{gathered} F(x)=8+11x-3x^2 \\ F(x+b)=8+11(x+b)-3(x+b)^2 \\ F(x+b)=8+11x+11b-3(x^2+2xb+b^2) \\ F(x+b)=8+11x+11b-3x^2-6xb-3b^2 \\ \\ \text{Since we cannot simplify further, we just rearrange} \\ \text{the final answer according to the degree of the terms} \\ F(x+b)=-3x^2-3b^2-6xb+11x+11b+8 \end{gathered}[/tex]c. Solve for F(-3)
Substitute x = -3
[tex]\begin{gathered} F(x)=8+11x-3x^2 \\ F(-3)=8+11(-3)-3(-3)^2 \\ F(-3)=8-33-3(9) \\ F(-3)=-25-27 \\ F(-3)=-52 \end{gathered}[/tex]Use the 'Permutations' formula to evaluate the expression P(27,3)
Answers
The permutation formula is given as:
[tex]P(n,k)=\frac{n!}{(n-k)!}[/tex]In this case n=27 and k=3; plugging the values in the formula we have:
[tex]P(27,3)=\frac{27!}{(27-3)!}=\frac{27!}{24!}=\frac{27\cdot26\cdot25\cdot24!}{24!}=27\cdot26\cdot25=17550[/tex]Therefore, we have that P(27,3)=17550
Look at the four company logos below.VolkswagenLincolnLexusRed Cross0♡+The logo for Volkswagen haslines of symmetry.The logo for Lincoln haslines of symmetry.The logo for Lexus haslines of symmetry.The logo for Red Cross has4lines of symmetry.:: 0.: 1:: 2
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Figures logos
Lines of symmetry = ?
Step 02:
We must analyze the logos to find the solution.
Volkswagen ===> 1 line of symmetry
Lincoln ===> 2 lines of symmetry
Lexus ===> 0 lines of symmetry
Red Cross ===> 4 lines of symmetry
That is the solution.
Answer:
VW: 1
Lincoln: 2
Lexus: 0
Red Cross: 2
Step-by-step explanation:
VW can be split in half once, and have the same thing son both sides.
Lincoln be split in half horizontally and vertically and be identical on both sides
Lexus cannot be split in half at all and be identical.
The red cross can be split horizontally and vertically and still have identical pieces.
-Hope this helped
Use elimination to solve each system of equations.4x + y = 233x - y = 12Use elimination to solve each system of equations.4x + y = 233x - y = 12
Answers
ANSWER
The solution is (5, 3)
EXPLANATION
To use elimination method, we have to subtract (or add) one equation from the other, in order to eliminate one of the variables. Then we'll have one equation with one variable. We solve it for that variable and then replace into one of the equations of the system to solve for the eliminated variable.
In these equations, we have +y in the first one and -y in the second one. We can add both equations to eliminate y:
[tex]\begin{gathered} (4x+y)+(3x-y)=23+12 \\ 4x+3x+y-y=35 \\ 7x=35 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 7x=35 \\ x=\frac{35}{7} \\ x=5 \end{gathered}[/tex]Now, we have to replace x = 5 into one of the equations and solve for y. Replacing in the first equation:
[tex]\begin{gathered} 4x+y=23 \\ 4\cdot5+y=23 \\ 20+y=23 \\ y=23-20 \\ y=3 \end{gathered}[/tex]The solution to this system is (5, 3)
Hi I need help with this question. Melissa starts with four packages of balloons and 8 single balloons. Her brother gave her 20 more balloons and three more packages. She now has twice the number of balloons she started with. Write and solve an equation to find how many balloons are in a package. How many balloons did Melissa start with?
Answers
Okay, here we have this:
Let's take the packages as (x), so we obtain:
Melissa Starts with: 4x+8 ballons (1)
Her brother gave her: 3x+20 ballons (2)
And as she now has twice the number of balloons she started with. This mean that:
2(4x+8)=(3x+20)+(4x+8)
Let's clear x in this equation:
8x+16=3x+20+4x+8
8x+16=7x+28
8x-7x=28-16
x=12
Finally we obtain that in a package are 12 ballons, now let's calculate How many balloons did Melisa start with?:
Remember that Melissa Starts with: 4x+8 ballons, so replacing x with 12, we obtain that Melissa Starts with: 4(12)+8=48+8=56.
Finally we obtain that Melissa Starts with 56 ballons.
Hi this is one of my exit ticket problem can you solve it please.
Answers
The triangles that are similar is A and B
Answer the statistical measures and create a box and whiskers plot for the followingset of data.4,4,5,5,5,6,6, 8, 9, 10, 12, 14, 14, 15, 17
Answers
Notice that the set of data is already ordered from lowest to highest, therefore the minimum value is 4 and the maximum value is 17.
The median is 8, the first quartile Q₁=5, and Q₃=14.
Then, the corresponding box and whiskers plot is:
How many distinct rearrangements of the letters in 'PUYGPGPYYUG' are there?
Answers
The answer is 92400
To solve this, we can count how many letters we have. There are 11 letters.
If those 11 letters were different from each other, the answer would be 11!
But we have letters that repeats:
3 P's
3 Y'2
3 G'2
2 U's
Since we want to know the quantity of distinct arrangements, we can divide by the repetition. This means:
[tex]\begin{gathered} 11!\text{ = total combinations} \\ \frac{11!}{3!\cdot3!\cdot3!\cdot2!}=\text{total distinct combinations} \end{gathered}[/tex]We divide by 3! times 3! times 3! times 2!, because we have 3P's, 3Y's, 3G's and 2U's
Then on the calculator write the division and give us the answer 92400
Find the prime factorization of 54 from least to greatest; then write it using exponents.
Answers
The prime factorization of 54 is
54 = 2 × 3 × 3 ×3
Using the exponential form of the prime factorization that is
54 = 2 × 3³
I don't know if -32 is greater or less than 15
Answers
Answer: -32 is less than 15.
Step-by-step explanation: 15 is greater than zero therefore it is not a negative number. -32 is less than 0 therefore it is a negative number. Negatives will always be less than positives.
Please I need help on this ASAP
Answers
The value of the function h(x) in part (a) is equal to h(x) = 2x.
The value of the function h(x) in part (b) is equal to h(x) = 5x/2 - 2.
How to determine the function h(x)?In this exercise, you are required to calculate the value of the function h(x), which is a product of the addition of function f(x) and function g(x). This ultimately implies that, the value of function h(x) can be calculated by adding function f(x) and function g(x) together.
For the first part (a), the value of function h(x) would be calculated as follows:
Function h(x) = Function f(x) + Function g(x)
Substituting the given parameters into the formula, we have;
Function h(x) = (x + 4) + (x - 4)
Function h(x) = x + 4 + x - 4
Function h(x) = 2x
For the second part (b), the value of function h(x) would be calculated as follows:
Function h(x) = Function f(x) + Function g(x)
Substituting the given parameters into the formula, we have;
Function h(x) = (2x - 4) + (x/2 + 2)
Function h(x) = 2x - 4 + x/2 + 2
Function h(x) = 5x/2 - 2.
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Lily drank 2 1/2 cartons of juice in the month of January. In the month of February, she drank twice as many cartons of juice as in January. How many cartons of juice did she drink in February?
Answers
Answer:
Lily drank 5 cartons of juice in February.
Explanation:
From the question, we're told that in January, Lily drank 2 1/2 cartons of juice and drank twice of that amount in February, so all we need to do is multiply the amount she drank in January by 2 to get the amount she drank in February.
Solving this, we'll have;
[tex]2\ast(2\frac{1}{2})=2\ast(\frac{5}{2})=5[/tex]Therefore, Lily drank 5 cartons of juice in February.
Alex has a box of chocolates which are all
flavoured with either caramel or raspberry.
The possible outcomes of Alex picking two
chocolates at random are shown in the tree
diagram below.
If both chocolates are the same flavour, what
is the probability that they are both
raspberry?
Give your answer as a fraction in its simplest
form.
Answers
Probability that they are both raspberry = 5/33
From the question, we have
probability that they are both raspberry = 5/12*4/11
=5/33
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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i need to find the independent variable and dependent and make a equation and find the output when input=10
Answers
The given situation is about the value of quarters and the number of quarters. If we think this through, we would deduct that the value of quarters depends on the number of quarters there are, for example, if there are 4 quarters, then the value is 1 dollar, and so on.
Hence,
The independent variable is the number of quarters.
The dependent variable is the value of the quarters.
The equation would be v = 0.25n.
If the input is 10, it means n = 10.
[tex]v=0.25n=0.25\cdot10=2.5[/tex]The output would be 2.5.
Find from first principles the derivative of f(x)= root of X with respect to x
Answers
To find:
The derivative of function f(x) using the first principle.
[tex]f(x)=\sqrt{x}[/tex]Solution:
By the first principle, the derivative of the function f(x) is given by:
[tex]f^{\prime}(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]So, the derivative of the given function can be obtained as follows:
[tex]\begin{gathered} f^{\prime}(x)=\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt{x}}{h} \\ =\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt{x}}{h}\times\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}} \\ =\lim_{h\to0}\frac{x+h-x}{h(\sqrt{x+h}+\sqrt{x})} \\ =\lim_{h\to0}\frac{h}{h(\sqrt{x+h}+\sqrt{x})} \\ =\lim_{h\to0}\frac{1}{(\sqrt{x+h}+\sqrt{x})} \\ =\frac{1}{\sqrt{x+0}+\sqrt{x}} \\ =\frac{1}{2\sqrt{x}} \end{gathered}[/tex]Thus, the derivative of the given function is:
[tex]f^{\prime}(x)=\frac{1}{2\sqrt{x}}[/tex]Please help. I am not sure how to go about this.
Answers
Solution:
(a) Given the functions:
[tex]\begin{gathered} f(x)=x-4 \\ \\ g(x)=x+4 \end{gathered}[/tex]Then:
[tex]\begin{gathered} f(g(x))=f(x+4) \\ \\ f(x+4)=x+4-4 \\ \\ f(g(x))=x \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} g(f(x))=g(x-4) \\ \\ g(x-4)=x-4+4 \\ \\ g(f(x))=x \end{gathered}[/tex]Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.
ANSWER: f and g are inverse of each other.
(b) Given:
[tex]\begin{gathered} f(x)=-\frac{1}{3x},x0 \\ \\ g(x)=\frac{1}{3x},x0 \end{gathered}[/tex]Then:
[tex]\begin{gathered} f(g(x))=f(\frac{1}{3x}) \\ \\ f(\frac{1}{3x})=-\frac{1}{3(\frac{1}{3x})} \\ \\ f(g(x))=-x \end{gathered}[/tex]Also,
[tex]\begin{gathered} g(f(x))=g(-\frac{1}{3x}) \\ \\ g(-\frac{1}{3x})=\frac{1}{3(-\frac{1}{3x})} \\ \\ g(f(x))=-x \end{gathered}[/tex]ANSWER: f and g are not inverses of each other.