Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$x \geq 4$$

Question 2

Given $$f(x) = x^2$ - 1$$ and $$g(x) = \sqrt{x+5}$$, what is the domain of the composite function $$(g \circ f)(x)$$?

Accepted Answer

$$x \leq -3 or$$ $$x \geq 3$$

Question 3

If $$f(x) is an $$even function, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = f(x)$$

Question 4

Given the piecewise function $$k(x) = \begin{cases} 2x+1, & x \leq 1 \ -x+3, & x \u003e 1 \end{cases}$$, what is $$k(2)$$?

Accepted Answer

$$5$$

Question 5

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - x$$

Question 6

Suppose $$f(x) = \sqrt{x+4}$$ and $$g(x) = x^2$. What is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \in \mathbb{R} ($$all real numbers)

Question 7

Given $$f(x) = -3x^4$ + 7x^2$ - 1$$, which of the following statements is true?

Accepted Answer

$$f(x) is an $$even function

Question 8

If $$h(x) = \begin{cases} x^2$, & x  3 \end{cases}$$, what is $$h(0)$$?

Accepted Answer

$$0$$

Question 9

Which of the following best describes the range of $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$[0, \infty)$$

Question 10

Given $$f(x) = x^2$ and g(x) = x+1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 11

A function $$f is $$said to be odd if:

Accepted Answer

$$f(-x) = -f(x)$$ for all x in the domain$

Question 12

Given $$f(x) = x^2$ - 4$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$(g \circ f)(x)$$?

Accepted Answer

$$x \leq -2 or$$ $$x \geq 2$$

Question 13

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

Accepted Answer

$$13$$

Question 14

Which of the following is the correct definition of the domain of the composite function $$(f \circ g)(x)$$?

Accepted Answer

The set of all $$x$$ such that $$x is in $$the domain of $$g$$ and $$g(x) is in $$the domain of $$f$$

Question 15

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

Accepted Answer

$$5$$

Question 16

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is (f$$ \circ g)(9)$$?

Accepted Answer

$$9$$

Question 17

Suppose $$f(x) = x^2$ and g(x) = x-2$. What is the value of x$ such that f(g(x)) = 9$?

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 18

Given $$f(x) = x^2$ and g(x) = x+1$, what is (f - g)(4$$)$$?

Accepted Answer

$$11$$

Question 19

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

Accepted Answer

$$12$$

Precalculus Study Guide: Functions, Domains, Ranges, and Composition

Study Guide - Practice Questions