Question 1

Given the function $$f(x) = 9x + 3$$, which of the following is the equation of its inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 3}{9}$$

Question 2

Which of the following graphs represents a function that is NOT one-to-one and therefore does NOT have an inverse function?

Accepted Answer

A parabola such as $$y = x^2$ - 12$$

Question 3

Suppose $$f(x) = 2x - 4$$ and $$g(x) = \frac{x+4}{2}. $$Are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

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

Question 4

Given $$f(x) = x^2$ - 1$$ with domain $$x \geq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x+1}$$

Question 5

A function $$f$$ passes the horizontal line test. What does this imply about $$f$$?

Accepted Answer

$$f is $$one-to-one and has an inverse function

Question 6

Given $$f(x) = (x+8)/6$$, what is the domain and range of $$f^{-1}(x$$)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 7

If $$f(x) = (x+14)/(x-7)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 7$$

Question 8

Given $$f(x) = x^3$ - 6$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x+6}$$

Question 9

Which of the following statements is TRUE about the graph of a function and its inverse?

Accepted Answer

The graph of the inverse is a reflection of the original function across the line $$y = x$$

Question 10

Given $$f(x) = 3x^2$ + 7$$ with domain $$x \geq 0$$, what is the range of $$f(x)$$?

Accepted Answer

$$[7, \infty)$$

Question 11

Suppose $$f(x) = (x+18)/(x-6). $$What is the $$x-$$value where $$f(x) is $$undefined?

Accepted Answer

$$x = 6$$

Question 12

Given $$f(x) = 2x + 4$$ and $$g(x) = \frac{x-4}{2}$$, what is $$f(g(x))$$?

Accepted Answer

$$x$$

Question 13

If $$f(x) = x^2$ - 12$$ and $$g(x) = \sqrt{x+12}$$, for $$x \geq -12$$, what is $$f(g(x))$$?

Accepted Answer

$$x$$

Question 14

Given $$f(x) = (7x+14)/(x-1)$$, what is the $$y-$$value where the graph of $$f(x)$$ intersects the line $$y = x$$?

Accepted Answer

$$y = 9.4772256$$

Question 15

Which of the following best describes the domain of $$f(x) = \sqrt{x+12}$$?

Accepted Answer

$$x \geq -12$$

Question 16

Given $$f(x) = (x+5)^3$, what is the inverse function f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x} - 5$$

Question 17

If $$f(x) = 3\sqrt{x} - 5$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 0$$

Question 18

Given $$f(x) = x^3$ + 12$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 19

Suppose $$f(x) = (x+8)/6$$ and $$g(x) = 6x - 8. $$What is $$g(f(x))$$?

Accepted Answer

$$x$$

Inverse Functions and One-to-One Functions: College Algebra Study Guidance

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