Q: Given $$f(x) = x^2$ + 1$$ and $$g(x) = x - 5$$, find $$\left(\frac{f}{g}\right)(x)$$ and its domain.

$$\frac{x^2$ + 1}{x - 5}$$, domain: $$x \neq 5$$

Q: If $$f(x) = \frac{5}{x-3}$$ and $$g(x) = \frac{1}{x}$$, find $$(f \circ g)(x)$$ and its domain.

$$\frac{5}{\frac{1}{x} - 3}$$, domain: $$x \neq 0$$ and $$x \neq \frac{1}{3}$$

Q: Given $$f(x) = \frac{1}{x-4}$$ and $$g(x) = \sqrt{x+4} - 1$$, find the domain of $$f(g(x)).$$

$$x \u003e -4$$ and $$\sqrt{x+4} - 1 \neq 4$$

Question 1

Given $$f(x) = \frac{7}{\sqrt{4 - x^2$}}$$, which of the following is the domain of $$f(x)$$?

Accepted Answer

$$x \in (-2, 2)$$

Question 2

If $$f(x) = 3 - |x|$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 3]$$

Question 3

Given $$f(x) = \sqrt{x-2}$$, which of the following is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 2$$

Question 4

Which of the following pairs of lines are perpendicular?

Accepted Answer

$$y = 2x - 1$$ and $$y = -\frac{1}{2}x + 5$$

Question 5

Martin has $$2000 invested in two different accounts. A low risk account pays 2$$\%$$ simple interest and a high risk account pays 9$$\%$$ simple interest. If he earned 320$ dollars in interest last year, how much is in each account?

Accepted Answer

$$800 in $$low risk, $$1200 in $$high risk

Question 6

Given the graph below, which $$x-$$values correspond to local maxima?

Accepted Answer

$$x = -2$$ and $$x = 2$$

Question 7

Given $$f(x) = x^2$ + 1$$ and $$g(x) = x - 5$$, find $$\left(\frac{f}{g}\right)(x)$$ and its domain.

Accepted Answer

$$\frac{x^2$ + 1}{x - 5}$$, domain: $$x 
eq 5$$

Question 8

Simplify $$(-3 + 5i)^2$.

Accepted Answer

$$-34 + 30i$$

Question 9

Solve $$6x^2 - 16x = -10$.

Accepted Answer

$$x = 1, x = \frac{5}{3}$$

Question 10

If $$f(x) = \frac{5}{x-3}$$ and $$g(x) = \frac{1}{x}$$, find $$(f \circ g)(x)$$ and its domain.

Accepted Answer

$$\frac{5}{\frac{1}{x} - 3}$$, domain: $$x 
eq 0$$ and $$x 
eq \frac{1}{3}$$

Question 11

Solve $$\sqrt{x - 1} = \sqrt{x + 4} - 1.$$

Accepted Answer

$$x = 5$$

Question 12

Solve $$|x - 5| \geq 3.$$

Accepted Answer

$$x \leq 2 or$$ $$x \geq 8$$

Question 13

Solve $$|1 - 2x| \leq 4$$ and graph the solution on a number line.

Accepted Answer

$$-1.5 \leq x \leq 2.5$$

Question 14

Given $$f(x) = \frac{1}{x-4}$$ and $$g(x) = \sqrt{x+4} - 1$$, find the domain of $$f(g(x)).$$

Accepted Answer

$$x \u003e -4$$ and $$\sqrt{x+4} - 1 
eq 4$$

Question 15

Simplify $$\frac{5 - 3i}{3 - 4i}.$$

Accepted Answer

$$\frac{3 + 11i}{25}$$

Question 16

Solve $$|3x - 4| + 7 = 12.$$

Accepted Answer

$$x = \frac{3}{3} or$$ $$x = \frac{11}{3}$$

Question 17

Given the function $$f(x) = x^3$ - 6x^2$ + 16x - 8$$, find the vertex, max or min value, the range, and the intervals of increasing and decreasing.

Accepted Answer

Vertex at $$x = 2$$, minimum value at $$f(2) = 0$$, range: $$[0, \infty)$$, increasing for $$x \u003e 2$$, decreasing for $$x \u003c 2$$

Precalculus Study Guide: Functions, Graphs, and Algebraic Techniques

Study Guide - Practice Questions

Study Guide - Flashcards