Question 1

Which of the following sets represents the Cartesian product $$A 	imes B$$ where $$A = \{1, 2\}$$ and $$B = \{a, b, c\}$$?

Accepted Answer

$$\{(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)\}$$

Question 2

Given the function $$f(x) = x^2$ - 2$$, which of the following statements is true about its invertibility?

Accepted Answer

It is not invertible because it is not one-to-one.

Question 3

Find the inverse of the function $$f(x) = \dfrac{x+1}{x-2}.$$

Accepted Answer

Question 4

Which of the following is the correct formula for the exponential function describing population growth?

Accepted Answer

$$P(t) = P_0$ e$$^{rt}$$

Question 5

If $$f(x) = 2x + 3$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 3$

Question 6

Which of the following is the correct change of base formula for logarithms?

Accepted Answer

$$\log_b M = \dfrac{\log_a M}{\log_a b}$$

Question 7

Express $$\log_b (MN) in $$terms of $$\log_b M$$ and $$\log_b N.$$

Accepted Answer

$$\log_b M + \log_b N$$

Question 8

Which of the following is the correct logarithmic form of the exponential equation $$a^x = M$$?

Accepted Answer

$$x = \log_a M$$

Question 9

If $$\log_2$ x = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 10

Which of the following is the correct expression for $$\log_b \left(\dfrac{M}{N}\right)$$?

Accepted Answer

$$\log_b M - \log_b N$$

Question 11

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 12

Which of the following is the correct property for $$\log_b (M^k)$$?

Accepted Answer

$$k \log_b M$$

Question 13

If $$f(x) = \dfrac{1}{x+1}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

Question 14

Which of the following is the correct exponential equation for $$\log_3$ x = 4$$?

Accepted Answer

$$x = 3^4$

Question 15

If $$f(x) = x^2$ and g(x) = x - 3$, find f(g(5$$))$$.

Accepted Answer

$$4$$

Question 16

Which of the following is the correct logarithmic property for $$\log_b \sqrt{M}$$?

Accepted Answer

$$\dfrac{1}{2} \log_b M$$

Question 17

Suppose the population of a city grows exponentially according to $$P(t) = 1000 e$$^{0.03t}$$. How long will it take for the population to double?

Accepted Answer

$$t = \dfrac{\ln 2}{0.03}$$

Question 18

Which of the following is the correct expression for $$\log_b \left(\dfrac{\sqrt{M}}{N^3$}\right)$$?

Accepted Answer

$$\dfrac{1}{2} \log_b M - 3 \log_b N$$

Question 19

If $$\log_{10} 2 \approx 0.3010$$ and $$\log_{10} 5 \approx 0.6990$$, what is $$\log_{10} 20$$?

Accepted Answer

$$1.0000$$

College Algebra Study Guide: Functions, Exponential & Logarithmic Equations, and Systems

Study Guide - Practice Questions