$x \neq \sqrt{2}$,\ x \neq -\sqrt{2}$

Question 1

Given the functions $f(x) = x^2 + 3x - 10$ and $g(x) = x - 2$, what is $f(g(x))$?

Accepted Answer

$(x-2)^2 + 3(x-2) - 10$

Question 2

If $f(x) = x + 4$ and $g(x) = x^2 - 3$, what is $(g \circ f)(x)$?

Accepted Answer

$(x+4)^2 - 3$

Question 3

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

Accepted Answer

$(x-2)^2 - 4 \geq -4$

Question 4

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

Accepted Answer

$4$

Question 5

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

Accepted Answer

$x > 0$ and $\sqrt{x} 
eq 2$

Question 6

Which of the following correctly expresses $h(x) = \sqrt{x-2}$ as a composition of two functions $f$ and $g$ such that $h(x) = (f \circ g)(x)$?

Accepted Answer

$f(x) = \sqrt{x},\ g(x) = x-2$

Question 7

Given $f(x) = x^2 + 3x - 10$ and $g(x) = x - 2$, what is $(g \circ f)(x)$?

Accepted Answer

$x^2 + 3x - 10 - 2$

Question 8

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

Accepted Answer

$7$

Question 9

Given $f(x) = \frac{1}{x^2 - 3x - 10}$, which of the following is a valid decomposition $f(x) = (f_1 \circ g_1)(x)$?

Accepted Answer

$f_1(x) = \frac{1}{x},\ g_1(x) = x^2 - 3x - 10$

Question 10

Suppose $f(x) = x^2$ and $g(x) = \sqrt{x-8}$. What is the domain of $(f \circ g)(x)$?

Accepted Answer

$x \geq 8$

Question 11

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

Accepted Answer

$\sqrt{x^2 + 2}$

Question 12

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

Accepted Answer

$\sqrt{x+1}$

Question 13

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

Accepted Answer

$x 
eq \sqrt{2}$,\ x 
eq -\sqrt{2}$

Question 14

If $f(x) = x^2 + 3x - 10$ and $g(x) = x - 2$, what is $(f \circ g)(3)$?

Accepted Answer

$-2$

Question 15

Given $f(x) = x + 3$ and $g(x) = x^2$, what is $(g \circ f)(2)$?

Accepted Answer

$25$

Question 16

Suppose $f(x) = \sqrt{x}$ and $g(x) = x^2 + 1$. What is $(f \circ g)(x)$?

Accepted Answer

$\sqrt{x^2 + 1}$

Question 17

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

Accepted Answer

$(x+1)^2$

Question 18

Given $f(x) = \frac{1}{x}$ and $g(x) = x^2 - 4$, what is the domain of $(f \circ g)(x)$?

Accepted Answer

$x 
eq 2,\ x 
eq -2$

Question 19

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

Accepted Answer

$x,\ x \geq 0$

Question 20

Which of the following is a correct decomposition of $h(x) = \frac{1}{x^2 - 3x - 10}$ as $h(x) = (f \circ g)(x)$?

Accepted Answer

$f(x) = \frac{1}{x},\ g(x) = x^2 - 3x - 10$

Function Composition and Decomposition in College Algebra

Study Guide - Practice Questions