Question 1

Let $$f(x) = 2x - 5$$ and $$g(x) = x^2$ - 3x + 8. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$2x^2 - 16x - 21$

Question 2

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

Accepted Answer

$$[3, \infty)$$

Question 3

If $$f(x) = x^5$ and g(x) = 2x - 3$, which function h(x$$)$$ can be written as (f$$ \circ g)(x)$$?

Accepted Answer

$$(2x - 3)^5$

Question 4

Let $$f(x) = 2x - 5$$ and $$g(x) = x^2$ - 3x + 8. $$What is $$(g \circ f)(x)$$?

Accepted Answer

$$4x^2 - 26x + 48$

Question 5

Given $$f(x) = \sqrt{x}$$ and $$g(x) = x - 3$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$\sqrt{x} - 3$$

Question 6

Which of the following best describes the domain of $$(g \circ f)(x)$$ for $$f(x) = \sqrt{x}$$ and $$g(x) = x - 3$$?

Accepted Answer

$$[0, \infty)$$

Question 7

Suppose $$f(x) = x^2$ and g(x$$) = \sin x$$. Which of the following is (f$$ \circ g)(x)$$?

Accepted Answer

$$(\sin x)^2$

Question 8

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

Accepted Answer

$$[0, \infty)$$

Question 9

A medical dosage formula is $$f(x) = 2x + 1$$, where $$x is $$the patient's weight in kg. If the patient's weight is given by $$g(t) = 0.5t + 10$$, where $$t is $$age in years, what is the dosage as a function of age?

Accepted Answer

$$f(g(t)) = 2(0.5t + 10) + 1 = t + 21$$

Question 10

Which statement is true about the domain of $$(f \circ g)(x)$$?

Accepted Answer

It consists of all $$x in $$the domain of $$g$$ such that $$g(x) is in $$the domain of $$f.$$

Question 11

If $$h(x) = \ln(2x - 1)$$, decompose $$h(x) as$$ $$(f \circ g)(x)$$ for suitable $$f$$ and $$g.$$

Accepted Answer

$$f(x) = \ln x$$, $$g(x) = 2x - 1$$

Question 12

Let $$f(x) = x^2$ and g(x) = x + 1$. What is (g$$ \circ f)(x)$$?

Accepted Answer

$$x^2 + 1$

Question 13

A chemical reaction rate is modeled by $$f(x) = 5x^2$, where x$ is concentration. If concentration over time is g(t) = 2t + 1$, what is the reaction rate as a function of time?

Accepted Answer

$$f(g(t)) = 5(2t + 1)^2$

Question 14

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

Accepted Answer

$$(f \circ g)(x) = x$$, domain $$[0, \infty)$$

Question 15

Which of the following is a valid decomposition of $$h(x) = \sin(3x) as$$ $$(f \circ g)(x)$$?

Accepted Answer

$$f(x) = \sin x$$, $$g(x) = 3x$$

Question 16

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

Accepted Answer

$$25$$

Question 17

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

Accepted Answer

$$(-\infty, -2] \cup [2, \infty)$$

Question 18

A population model is $$f(x) = 1000e$$^{0.02x}$$, where x$ is years since 2000. If g(t) = t - 2000$, where t$ is the actual year, what is the population as a function of t$?

Accepted Answer

$$1000e^{0.02(t - 2000)}$$

Section 2.3: The Composition of Functions – Precalculus Study Notes

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