Question 1

Solve the polynomial inequality $$x^3$$ - $$3x^2 + 2x$$ \geq 0$$. Which of the following is the correct solution set?

Accepted Answer

$$[0, 1] \cup [2, \infty)$$

Question 2

Given the rational inequality $$\frac{x+1}{x-4} \leq 0$$, what is the solution set?

Accepted Answer

$$(-\infty, -1] \cup (1, 4)$$

Question 3

If $$f(x) = x^2$ and g(x) = 3x - 1$, what is the product function f(x$$) \cdot g(x)$$?

Accepted Answer

$$x^2(3x - 1$$) = $$3x^3$$ - $$x^2$$

Question 4

Let $$f(x) = \frac{12}{x}$$ and $$g(x) = \sqrt{x}. $$What is $$(f \circ g)(4)$$?

Accepted Answer

$$6$$

Question 5

Given $$f(x) = \sqrt{x+1}$$ and $$g(x) = x - 16$$, what is the domain of $$f + g$$?

Accepted Answer

$$[-1, \infty)$$

Question 6

If $$f(x) = x^2$ and g(x) = 3x - 1$, what is the quotient function $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$\frac{x^2$}{3x - 1}$$

Question 7

Find the intersection of the intervals $$[0, \infty)$$ and $$(-\infty, 5].$$

Accepted Answer

$$[0, 5]$$

Question 8

Given $$f(x) = \sqrt{x}$$ and $$g(x) = 4 - x$$, what is the domain of $$f + g$$?

Accepted Answer

$$[0, 4]$$

Question 9

Let $$f(x) = \frac{x+2}{\sqrt{4-x}}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, 4)$$

Question 10

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

Accepted Answer

$$9$$

Question 11

Given $$f(x) = \sqrt{x+1}$$ and $$g(x) = x - 16$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$[-1, 16) \cup (16, \infty)$$

Question 12

Which of the following is the correct domain for the function $$f(x) = \frac{x+2}{\sqrt{4-x}}$$?

Accepted Answer

$$(-\infty, 4)$$

Question 13

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

Accepted Answer

$$x^2 - 3x - 1$

Question 14

Let $$f(x) = \frac{12}{x}$$ and $$g(x) = \sqrt{x}. $$What is $$(g \circ f)(4)$$?

Accepted Answer

$$\sqrt{12/4} = \sqrt{3}$$

Question 15

Given $$f(x) = \sqrt{x}$$ and $$g(x) = 4 - x$$, what is the domain of $$f \cdot g$$?

Accepted Answer

$$[0, 4]$$

Question 16

Find the intersection of the intervals $$(-\infty, -2) \cup (-2, \infty)$$ and $$(-4, 0).$$

Accepted Answer

$$[-4, -2) \cup (-2, 0)$$

Question 17

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

Accepted Answer

$$25$$

Question 18

Given $$f(x) = \sqrt{x+1}$$ and $$g(x) = x - 16$$, what is the domain of $$f - g$$?

Accepted Answer

$$[-1, \infty)$$

Question 19

Let $$f(x) = \frac{x+2}{\sqrt{4-x}}$$ and $$g(x) = \sqrt{x}. $$What is the domain of $$f \cdot g$$?

Accepted Answer

$$[0, 4)$$

Algebra of Functions, Composite Functions, and Inequalities: Study Guide

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