Question 1

Which of the following functions is one-to-one on its entire domain?

Accepted Answer

$$y = x^3$

Question 2

Given $$f(x) = 5x - 7$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{5}$$

Question 3

If $$f(1) = 5$$, what is $$f^{-1}(5$$)$$?

Accepted Answer

$$1$$

Question 4

Which of the following best describes the domain of the function $$f(x) = \sqrt{3x - 6}$$?

Accepted Answer

$$x \geq 2$$

Question 5

Which property of logarithms allows you to write $$\ln(ab) as$$ $$\ln a + \ln b$$?

Accepted Answer

Product Rule

Question 6

Expand the following logarithmic expression using properties of logarithms: $$\ln\left(\frac{x(x^2$ + 2)}{3x + 1}\right)$$

Accepted Answer

$$\ln x + \ln(x^2$ + 2) - \ln(3x + 1)$$

Question 7

Which of the following is the correct inverse for $$f(x) = 8 - \frac{1}{3}(5x^3$ + 7)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{3(8 - x) - 7}/5$$

Question 8

Which of the following statements about the natural logarithmic function $$f(x) = \ln x is $$true?

Accepted Answer

Its domain is $$(0, \infty)$$ and its range is $$(-\infty, \infty).$$

Question 9

Which of the following is the correct condensed form of $$3\ln(3t^2$ - 1) - \ln(t + 1)$$?

Accepted Answer

$$\ln\left(\frac{(3t^2$ - 1)^3$}{t + 1}\right)$$

Question 10

If $$f(x) is a $$one-to-one function with domain $$D$$ and range $$R$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$R$$

Question 11

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

Accepted Answer

The graph of $$y = f$$^{-1}$$(x) is a $$reflection of $$y = f(x)$$ about the line $$y = x.$$

Question 12

Evaluate $$\arcsin(\sin \pi).$$

Accepted Answer

$$0$$

Question 13

Which of the following is the correct value for $$\arccos(-1)$$?

Accepted Answer

$$\pi$$

Question 14

Which of the following is NOT a property of the natural logarithm?

Accepted Answer

$$\ln(a + b) = \ln a + \ln b$$

Question 15

Which of the following is the correct value for $$\arctan(-1)$$?

Accepted Answer

$$-\frac{\pi}{4}$$

Question 16

Which of the following functions is NOT one-to-one?

Accepted Answer

$$y = x^2$

Question 17

Suppose $$f(x) is a $$one-to-one function. If $$f^{-1}(8) = -10$, what is f(-10$$)$$?

Accepted Answer

$$8$$

Question 18

Which of the following best describes the range of the exponential function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 19

Which of the following is the correct application of the reciprocal rule for logarithms?

Accepted Answer

$$\ln\left(\frac{1}{x}\right) = -\ln x$$

1.6

Study Guide - Practice Questions