Question

This set of points is on the graph of a function.
{(−3, 9), (−1, 1), (0, 0), (2, 4)}
Which points are on the graph of the inverse?
Select each correct answer.
(0, 0)
(−9, 3)
(4, 2)
(1, −1)

What is the inverse of f(x)=4x+3 ?
f^−1(x)=1/4x−3/4
f^−1(x)=−1/4x+3/4
f^−1(x)=4x−3
f^−1(x)=−4x−3

What is the inverse of the function?
g(x)=−4/3x+2

g^−1(x)=−4/3x−2
g^−1(x)=3/4x+2/3
g^−1(x)=−3/4x+3/2
g^−1(x)=4/3x−2

Which functions are invertible?
Select each correct answer. (has pictures)

A.
B.
C.
D.

What is the inverse of f(x)=x4+7 for x≥0 where function g is the inverse of function f?



g(x)=x+7√4 , x≥−7

g(x)=x√4+7 , x≥0

g(x)=x−7√4,  x≥7

g(x)=x√4−7 , x≥0

Answer 1

Problem 1)

(-3,9) is one point on the original function, so (9,-3) is on the inverse. We swap x and y. The point (9,-3) isn't listed so we move onto the next.

(-1,1) is on the original so (1,-1) is on the inverse. Again we swap x and y. Choice D matches with this. So D is one of the answers.

Choice A is also an answer since (0,0) swaps to (0,0)

Choice C is also an answer since (2,4) swaps to (4,2)

In summary, the answers are A, C, D

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Problem 2)
Replace f(x) with y. Swap x and y. Then solve for y

f(x) = 4x+3
y = 4x+3
x = 4y+3
x-3 = 4y+3-3
x-3 = 4y
4y = x-3
4y/4 = (x-3)/4
y = (x-3)/4
y = x/4-3/4
y = (1/4)x-3/4

which matches with choice A, so choice A is the answer

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Problem 3)
Replace g(x) with y. Swap x and y. Then solve for y

g(x) = (-4/3)x + 2
y = (-4/3)x + 2
x = (-4/3)y + 2
x-2 = (-4/3)y + 2-2
x-2 = (-4/3)y
(-3/4)(x-2) = (-3/4)(-4/3)y
(-3/4)(x-2) = y
y = (-3/4)(x-2)
y = (-3/4)x+(-3/4)(-2)
y = (-3/4)x+3/2 ... answer is choice C

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Problem 4)

The first two are invertible while the last two are not. The last two fail the horizontal line test so they don't have an inverse.

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Problem 5)

It's a bit tricky to determine what the answer choices are saying but I'm assuming they are referring to fourth roots. If so, then we have

f(x) = x^4+7
y = x^4+7
x = y^4+7
x-7 = y^4+7-7
x-7 = y^4
y^4 = x-7
FourthRoot(y^4) = FourthRoot(x-7)
y = FourthRoot(x-7)

which is written as $\sqrt[4]{x-7}$