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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 11. (page 256)

Find the value for the given functions $f, g$ .
$f (x) = 2 x, g (x) = 3 x^{2} + 1$
(a) $(f 鈭� g) (4)$ (b) $(g 鈭� f) (2)$ (c) $(f 鈭� f) (1)$ (d) $(g 鈭� g) (0)$ .

Short Answer

Expert verified

The value is (a) 98 (b) 49 (c) 4 (d) 4.

Step by step solution

01

Part (a) Step 1. Given Information.

Find the value for the given functions $f, g$ .

localid="1646893203856" $f (x) = 2 x, g (x) = 3 x^{2} + 1$ .

02

Part (a) Step 2. Evalaution of a functional value.

The functional value is

(a) $(f 鈭� g) (4) = f (g (4)) = f (49) = 98$ .

03

Part (b) Step 1. Given Information.

Find the value for the given functions $f, g$

role="math" localid="1646893389780" $f (x) = 2 x, g (x) = 3 x^{2} + 1$ .

04

Part (b) Step 2. Evalaution of a functional value.

The value of the function is

$(g 鈭� f) (2) = g (f (2)) = g (4) = 49$ .

05

Part (c) Step 1. Given Information.

Find the value for the given functions $f, g$

$f (x) = 2 x, g (x) = 3 x^{2} + 1$ .

06

Part (c) Step 2. Evalaution of a functional value.

The value of the function is

$(f 鈭� f) (1) = f (f (1)) = f (2) = 4$ .

07

Part (d) Step 1. Given Information.

Find the value for the given functions $f, g$

f (x) = 2 x, g (x) = 3 x^{2} + 1

.

08

Part (d) Step 2. Evalaution of a functional value.

The value of the function is

$(g 鈭� g) (0) = g (g (0)) = g (1) = 4$ .

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Most popular questions from this chapter

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{2 x - 3}{x + 4}$

the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{x^{2} - 4}{2 x^{2}} x > 0$

A function $f$ has an inverse function. If the graph of $f$ lies in quadrant II, in which quadrant does the graph of $f^{- 1}$ lie?

True or False. The domain of the composite function $(f 鈭� g) (x)$ is the same as the domain of $g (x)$ .

A function $f$ has an inverse function. If the graph of $f$ lies in quadrant I in which quadrant does the graph of $f^{- 1}$ lie?

See all solutions

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