Q: Given $$f(x) = 2x + 3$$ and $$g(x) = x^2$ - 1$$, what is $$(f \circ g)(2)$$?

$$f(g(2)) = f(3) = 2 \times 3 + 3 = 9$$

Q: Suppose $$f(x) = \dfrac{1}{x-3}$$ and $$g(x) = x+2. $$What is $$(f \circ g)(x)$$ and its domain?

$$(f \circ g)(x) = \dfrac{1}{x-1}$$, domain: $$x \neq 1$$

Q: Let $$f(x) = \sqrt{x-1}$$ and $$g(x) = x^2$. What is the domain of (f$$ \circ g)(x)$$?

$$\{x \mid x \leq -1 \text{ or } x \geq 1\}$$

Q: Given $$f(x) = x^2$ and g(x) = 2x + 1$, find (g$$ \circ f)(-3)$$.

$$g(f(-3)) = g(9) = 2 \times 9 + 1 = 19$$

Q: If $$f(x) = \dfrac{1}{x}$$ and $$g(x) = \dfrac{1}{x}$$, what is $$(f \circ g)(x)$$ and its domain?

$$(f \circ g)(x) = x$$, domain: $$x \neq 0$$

Q: If $$f(x) = \dfrac{1}{x-1}$$ and $$g(x) = \dfrac{1}{x-2}$$, what is the domain of $$(f \circ g)(x)$$?

$$\{x \mid x \neq 2, x \neq 3\}$$

Question 1

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

Accepted Answer

$$f(g(2)) = f(3) = 2 	imes 3 + 3 = 9$$

Question 2

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

Accepted Answer

$$\{x \mid x^2$ 
eq 2\}$$

Question 3

Let $$f(x) = 5x - 1$$ and $$g(x) = 3x^2$. Find (g$$ \circ f)(-2)$$.

Accepted Answer

$$g(f(-2)) = g(-11) = 3(-11)^2$ = 363$$

Question 4

Suppose $$f(x) = x^2$ + 2x - 5$$ and $$g(x) = 3x + 1. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$9x^2 + 12x - 2$

Question 5

Given $$f(x) = \dfrac{1}{x+3}$$ and $$g(x) = x-2$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$\{x \mid x 
eq -1\}$$

Question 6

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

Accepted Answer

$$\{x \mid x \geq 4\}$$

Question 7

Let $$f(x) = \dfrac{1}{x}$$ and $$g(x) = x^2$ - 9. $$What values must be excluded from the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 8

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

Accepted Answer

$$\{x \mid x \in \mathbb{R}\}$$

Question 9

Suppose $$f(x) = \dfrac{1}{x-3}$$ and $$g(x) = x+2. $$What is $$(f \circ g)(x)$$ and its domain?

Accepted Answer

$$(f \circ g)(x) = \dfrac{1}{x-1}$$, domain: $$x 
eq 1$$

Question 10

If $$f(x) = 2x - 5$$ and $$g(x) = \dfrac{x+5}{2}$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$x$$

Question 11

A medical test uses the function $$f(x) = \ln(x) to $$analyze the concentration $$x of a $$drug in the bloodstream, where $$x \u003e 0. If $$the concentration is modeled by $$g(t) = 5e$$^{-0.2t}$$, where t$ is time in hours, what is the domain of (f$$ \circ g)(t)$$?

Accepted Answer

$$\{t \mid t \in \mathbb{R}\}$$

Question 12

Let $$f(x) = \sqrt{x-1}$$ and $$g(x) = x^2$. What is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$\{x \mid x \leq -1 	ext{ or } x \geq 1\}$$

Question 13

Given $$f(x) = x^2$ and g(x) = 2x + 1$, find (g$$ \circ f)(-3)$$.

Accepted Answer

$$g(f(-3)) = g(9) = 2 	imes 9 + 1 = 19$$

Question 14

If $$f(x) = \dfrac{1}{x}$$ and $$g(x) = \dfrac{1}{x}$$, what is $$(f \circ g)(x)$$ and its domain?

Accepted Answer

$$(f \circ g)(x) = x$$, domain: $$x 
eq 0$$

Question 15

A chemical reaction's rate is modeled by $$f(x) = \sqrt{x}$$, where $$x is $$the concentration of a reactant. If the concentration over time is $$g(t) = t^2$ + 1$$, what is the domain of $$(f \circ g)(t)$$?

Accepted Answer

$$\{t \mid t \in \mathbb{R}\}$$

Question 16

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

Accepted Answer

$$\{x \mid x \geq 0\}$$

Question 17

Let $$f(x) = x^2$ and g(x) = x+1$. Find all x$ such that (f$$ \circ g)(x) = 0$$.

Accepted Answer

$$x = -1$$

Question 18

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

Accepted Answer

$$\{x \mid x 
eq 2, x 
eq 3\}$$

Question 19

A population model uses $$f(x) = \ln(x)$$ and $$g(t) = 100e$$^{0.05t}$$. What is the composite function (f$$ \circ g)(t)$$?

Accepted Answer

$$\ln(100) + 0.05t$$

Composite Functions: Definitions, Evaluation, and Domain (Section 6.1 Study Notes)

Study Guide - Practice Questions

Study Guide - Flashcards