Q: Given the functions $$f(x) = \frac{2x}{x-1}$$ and $$g(x) = \frac{x-2}{x}$$, what is the domain of $$f \circ g$$?

$$x \neq 0,\ x \neq 2,\ x \neq 1$$

Q: Joe wants to double his $$750 in a savings account that compounds interest daily. Which equation should he use to solve for the required interest rate r$ if he wants to double his money in 7 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

$$1500 = 750(1 + \frac{r}{365}$$)^{365 \times 7}$$

Question 1

Given the functions $$f(x) = \frac{2x}{x-1}$$ and $$g(x) = \frac{x-2}{x}$$, what is the domain of $$f \circ g$$?

Accepted Answer

$$x 
eq 0,\ x 
eq 2,\ x 
eq 1$$

Question 2

Which of the following sets represents the range of the relation $$\{(-1,4), (3,4), (4,-7), (7,4), (5,-7)\}$$?

Accepted Answer

$$\{4, -7\}$$

Question 3

Given $$f(x) = \frac{2x+1}{x-2}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

Question 4

Which of the following best describes the horizontal asymptote of $$f(x) = (\frac{1}{x})^2$ - 2$$?

Accepted Answer

$$y = -2$$

Question 5

What is the solution to $$\log_3$(18) - \log_3$(9)$$?

Accepted Answer

$$\log_3$(2)$$

Question 6

If $$f(x) = \log_2$(x^2 - 9$$)$$, what is the domain of f$?

Accepted Answer

$$(-\infty, -3) \cup (3, \infty)$$

Question 7

Expand $$\log_4$\left(\frac{x^5$}{y^2$ z^7$}\right) as a $$sum or difference of logarithms.

Accepted Answer

$$5\log_4$(x) - 2\log_4$(y) - 7\log_4$(z)$$

Question 8

A laboratory has 11.3 mg of Re-188, which has a half-life of 16.9 hours. How much will remain after 10 hours? (Use $$A = A_0$ (1/2$$)^{t/h}$$)

Accepted Answer

$$7.85 mg$$

Question 9

Solve for $$x$$: $$27^{x-1}$$ $$(3^{x+1})^2$ = 1$

Accepted Answer

$$x = -1$$

Question 10

Joe wants to double his $$750 in a savings account that compounds interest daily. Which equation should he use to solve for the required interest rate r$ if he wants to double his money in 7 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$1500 = 750(1 + \frac{r}{365}$$)^{365 	imes 7}$$

Question 11

Which of the following is the correct simplification for $$2\ln(e^4$)$$?

Accepted Answer

$$8$$

Question 12

Given $$f(x) = \log_2$(x+2) + 1$$, what is the vertical asymptote of the graph?

Accepted Answer

$$x = -2$$

Question 13

Which of the following is the correct solution to $$3^{2x} = 4^x$?

Accepted Answer

$$x = 0$$

Question 14

If $$f(x) = x^2$ - 3x$$ and $$g(x) = 2x - 1$$, what is $$f(g(1))$$?

Accepted Answer

$$-2$$

Question 15

Which of the following is the correct single logarithm for $$\frac{1}{3}\ln(x^2$ - 3x) - 2\ln(x+1)$$?

Accepted Answer

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

Question 16

Which of the following is the correct domain for the function $$f(x) = \log_2$(x^2 - 9$$)$?

Accepted Answer

$$(-\infty, -3) \cup (3, \infty)$$

Question 17

Which of the following is the correct solution for $$\log_2$(x) + \log_2$(x-2) = 1$$?

Accepted Answer

$$x = 4$$

Question 18

Which of the following is the correct simplified form of $$\log_2$(18) - \log_2$(9)$$?

Accepted Answer

$$\log_2$(2)$$

Question 19

If $$f(x) = x^2$ - 3x$$ and $$g(x) = 2x - 1$$, what is $$f(g(x))$$?

Accepted Answer

$$4x^2 - 14x + 10$

Precalculus Exam 4 Review: Functions, Logarithms, Exponentials, and Applications

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