$$\{x : x \neq 0, x \neq -6\}$$

Question 1

Which of the following is the correct domain of the function $$f(x) = \ln\left(\frac{x-1}{x+1}\right)$$?

Accepted Answer

$$(-\infty, -1) \cup (1, \infty)$$

Question 2

Given $$f(x) = \frac{3}{x+2}$$, which of the following is the correct inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{3}{x-2}$$

Question 3

For the function $$f(x) = 2$$^{-x}$$ - 4$$, what is the horizontal asymptote?

Accepted Answer

$$y = -4$$

Question 4

Solve for $$x$$: $$\log_3$(5x - 16) = 2.$$

Accepted Answer

$$x = 5$$

Question 5

Which of the following expresses $$\frac{2}{3} \ln 8 - \ln(5^2$ - 1) as a $$single logarithm in simplest form?

Accepted Answer

$$\ln\left(\frac{1}{6}\right)$$

Question 6

Find the domain of $$f(x) = \ln(x + 3).$$

Accepted Answer

$$(-3, \infty)$$

Question 7

If $$f(x) = x + \frac{1}{x}$$ and $$g(x) = 1 - x$$, what is $$(f \circ g)(0)$$?

Accepted Answer

$$	ext{undefined}$$

Question 8

Which of the following is the correct solution set for $$e^{2x} - 1 = 2e^x$?

Accepted Answer

$$\{\ln(1 + \sqrt{2})\}$$

Question 9

Given $$f(x) = \frac{x}{x+3}$$ and $$g(x) = \frac{2}{x}$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$\{x : x 
eq 0, x 
eq -6\}$$

Question 10

Which of the following is the correct range of $$f(x) = \frac{3}{x+2}$$?

Accepted Answer

$$\{y : y 
eq 0\}$$

Question 11

Solve for $$x$$: $$25^x - 8 \cdot 5^x + 16 = 0.$$

Accepted Answer

$$x = \log_5$ 4$$

Question 12

Which of the following is the correct inverse of $$f(x) = \ln(x + 3)$$?

Accepted Answer

$$f^{-1}(x) = e^x - 3$

Question 13

For $$f(x) = 2$$^{-x}$$ - 4$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -3)$$

Question 14

Solve for $$x$$: $$\ln(x + 6) - \ln(x - 4) = \ln x.$$

Accepted Answer

$$x = 6$$

Question 15

Which of the following is the correct solution set for $$(\log_3$ x)^2$ - 3 \log_3$ x = 10$$?

Accepted Answer

$$\{243, \frac{1}{9}\}$$

Question 16

If $$f(x) = 3x^2$ - 7$$ and $$g(x) = 2x - a$$, for what value of $$a$$ does the graph of $$f \circ g$$ cross the $$y-$$axis at $$68$$?

Accepted Answer

$$a = -5$$

Question 17

Which of the following is the vertical asymptote of $$f(x) = \ln(x + 3)$$?

Accepted Answer

$$x = -3$$

Question 18

If $$f(x) = x + \frac{1}{x}$$ and $$g(x) = 1 - x$$, what is $$(g \circ f)(1)$$?

Accepted Answer

$$-1$$

Question 19

Solve for $$x$$: $$2^{1-x}$$ = $$3^{x+1}.$$

Accepted Answer

$$x = \frac{1 - \log_2$ 3}{1 + \log_2$ 3}$$

Precalculus Test 4 Study Guide: Inequalities, Functions, Logarithms, and Exponentials

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