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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. 17 (page 256)

Find for the given functions $f, g$ such that
$f (x) = |x|, g (x) = \frac{1}{x^{2} + 1}$ .
Find : (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) $\frac{1}{17}$ (b) $\frac{1}{5}$ (c) 1 (d) $\frac{1}{2}$ .

Step by step solution

01

Part (a) Step 1. Given Information.

The given functions are :

$f (x) = |x|, g (x) = \frac{1}{x^{2} + 1}$ .

02

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

The functional value is :

(a) $(f 鈭� g) (4) = f (g (4)) = f (\frac{1}{17}) = \frac{1}{17}$ .

03

Part (b) Step 1. Given Information.

The given function be

$f (x) = |x|, g (x) = \frac{1}{x^{2} + 1}$ .

04

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

The value of the function be

$(g 鈭� f) (2) = g (f (2)) = g (2) = \frac{1}{5}$ .

05

Part (c) Step 1. Given Information.

The given function be

$f (x) = |x|, g (x) = \frac{1}{x^{2} + 1}$ .

06

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

The value of the function be

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

07

Part (d) Step 1. Given Information.

The given function be

$f (x) = |x|, g (x) = \frac{1}{x^{2} + 1}$ .

08

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

The value of the function be

$(g 鈭� g) (0) = g (g (0)) = g (1) = \frac{1}{2}$ .

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