Quiz about Inverses Using Function Composition

Question 1

When using composition to verify 2 functions are inverses, g(f(x)) and f(g(x)) must equal

Accepted Answer

x

Answer

y

Answer

f(x)

Answer

g(x)

Question 2

The inverse of the function f(x) is written as ...

Accepted Answer

f -1(x)

Answer

f 2(x)

Answer

f '(x)

Answer

f +(x)

Question 3

What are the missing values if g(x)=f^-1(x)?

Accepted Answer

(9,-5)

Answer

(-9,-5)

Answer

(5,9)

Answer

(-9,5)

Question 4

Verify if the functions are inverses using composition of functions:

Accepted Answer

Yes, they are inverses because $$f\circ g(x)=x=g\circ f\left(x\right)$$

Answer

Yes, they are inverses because $$\left(g(f(x))=f(g(x)\right)=0$$

Answer

No they are not inverses because $$f(g(x))=x+2$$

Answer

No, they are not inverses because $$f\left(x ight) e g\left(x ight)$$

Question 5

Solve the equation involving the inverse function: $$f^{-1}(f(x)) = 12$$ .

Accepted Answer

$$x = 12$$

Answer

$$x = f(12)$$

Answer

$$x = f^{-1}(12)$$

Answer

$$x = 0$$

Question 6

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

Accepted Answer

False

Answer

True

Question 7

If $$f(x) = x^2$$ and $$g(x) = \sqrt{x}$$ , are $$f\left(x\right)$$ and $$g\left(x\right)$$ inverse functions?

Accepted Answer

Yes, $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Answer

No, $$f(g(x)) eq x$$ and $$g(f(x)) eq x$$

Answer

Yes, $$f(g(x)) = x$$ but $$g(f(x)) eq x$$

Answer

No, $$f(g(x)) eq x$$ but $$g(f(x)) = x$$

Question 8

Are these functions inverses of each other?

$$h\left(x\right)=-\frac{1}{3}x+\frac{1}{3}$$

$$f\left(x\right)=-3x+1$$

Accepted Answer

Yes

Answer

No

Question 9

What is the composition of a function and its inverse, $$f(f^{-1}(x))$$ ?

Accepted Answer

$$x$$

Answer

$$f(x)$$

Answer

$$f^{-1}(x)$$

Answer

$$0$$

Question 10

The algebraic process used to formally prove that two functions are inverses is called:

Accepted Answer

composition of functions

Answer

function notation

Answer

function multiplication

Answer

combined functions

Question 11

Given the function represented by the table, identify the function that is the inverse.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 12

Identify the sets of inverse functions by using their result from composition of the functions.

Accepted Answer

$$f\left(g\left(x\right)\right)=x$$

Answer

$$f\left(g\left(x\right)\right)=2x-1$$

Answer

$$f\left(g\left(x\right)\right)=\frac{1}{3}x-3$$

Answer

$$f\left(g\left(x\right)\right)=x^2-2$$

Question 13

Use Composition to determine if they given functions are inverses.

Accepted Answer

Not Inverse Functions

Answer

Inverse Functions

Question 14

Use Composition to determine if they given functions are inverses.

Accepted Answer

Inverse Functions

Answer

Not Inverse Functions

Question 15

What is the best description?

Accepted Answer

They are inverse functions.

Answer

They are both functions, but not inverse functions.

Answer

They are reflected over y=x, but they are not both functions.

Answer

They are not reflected over y=x, and they are not both functions.

Question 16

Which is f ^-1(x)?

Accepted Answer

f^-1(x) = 5x - 3

Answer

f^-1(x) = 5x + 3

Answer

f^-1(x) = 5x - 15

Answer

f^-1(x) = 1/5(x) + 3/5

Question 17

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)). Are the two functions inverses of each other?

Accepted Answer

x + 20 ; No, they are not inverses

Answer

x + 20 ; Yes they are inverses

Answer

x ; Yes they are inverses

Answer

x ; No, they are not inverses

Inverses Using Function Composition

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