Question 1

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

Accepted Answer

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

Question 2

If $$f(x) = x^3$ + 1$$ models the temperature (in $$^\circC) of a $$chemical reaction after $$x$$ minutes, how many minutes will it take for the temperature to reach $$28^\circC$$?

Accepted Answer

$$x = 3$$

Question 3

Which of the following best describes the domain and range of the function $$f(x) = x^3$ + 1$$?

Accepted Answer

Domain: $$x \in \mathbb{R}$$, Range: $$y \in \mathbb{R}$$

Question 4

Suppose $$f(x) = x^3$ + 1$$ and $$g(x) = \sqrt[3]{x - 1}. $$What is $$f(g(10))$$?

Accepted Answer

$$10$$

Question 5

If $$f(x) = x^3$ + 1$$, which of the following statements is true about $$f$$?

Accepted Answer

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

Question 6

Given $$f(x) = x^3$ + 1$$, what is $$f^{-1}(9$$)$$?

Accepted Answer

$$2$$

Question 7

If $$f(x) = x^3$ + 1$$ and $$f^{-1}(x$$) = \sqrt[3]{x - 1}$$, what is f(f$$^{-1}$$(x))$$?

Accepted Answer

$$x$$

Question 8

A scientist uses the function $$f(x) = x^3$ + 1 to $$model the volume (in liters) of a gas after $$x$$ hours. If the volume is $$65$$ liters, how many hours have passed?

Accepted Answer

$$x = 4$$

Question 9

Which of the following compositions verifies that $$f^{-1}(x$$)$$ is the inverse of f(x$$)$$ for f(x$$) = $$x^3 + 1$?

Accepted Answer

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

Question 10

If $$f(x) = x^3$ + 1$$, what is the $$y-$$intercept of the graph of $$f(x)$$?

Accepted Answer

$$(0, 1)$$

Inverse Functions: Finding the Equation of the Inverse

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