Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 18. (page 256)

Find for the given functions $f, g$ such that
$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .
Find : (a)role="math" localid="1646303014287" $(f 鈭� g) (4)$ (b) $(g 鈭� f) (2)$ (c) $(f 鈭� f) (1)$ (d) $(g 鈭� g) (0)$ .

Short Answer

Expert verified

The value is (a) $\frac{11}{6}$ (b) $\frac{3}{2}$ (c) 1 (d) $\frac{12}{17}$ .

Step by step solution

Part (a) Step 1. Given Information.

The given functions are :

$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .

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

The functional value is :

(a) $(f 鈭� g) (4) = f (g (4)) = f (\frac{1}{6}) = (|\frac{1}{6} - 2|) = \frac{11}{6}$ .

Part (b) Step 1. Given Information.

The given function be

$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .

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

The value of the function be

$(g 鈭� f) (2) = g (f (2)) = g (0) = \frac{3}{2}$ .

Part (c) Step 1. Given Information.

The given function be

$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .

Part (c) Evaluation of a functional value.

The value of the function be

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

Part (d) Given Information.

The given function be

$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .

Part (d) Evaluation of a functional value.

The value of the function be

$(g 鈭� g) (0) = g (g (0)) = g (\frac{3}{2}) = \frac{3}{2 + \frac{9}{4}} = \frac{12}{17}$ .

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91影视

Find for the given functions $f, g$ such that
$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .
Find : (a)role="math" localid="1646303014287" $(f 鈭� g) (4)$ (b) $(g 鈭� f) (2)$ (c) $(f 鈭� f) (1)$ (d) $(g 鈭� g) (0)$ .

Short Answer

Step by step solution

Part (a) Step 1. Given Information.

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

Part (b) Step 1. Given Information.

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

Part (c) Step 1. Given Information.

Part (c) Evaluation of a functional value.

Part (d) Given Information.

Part (d) Evaluation of a functional value.

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91影视

Find for the given functionsf,gsuch thatfx=x-2,gx=3x2+2.Find : (a)role="math" localid="1646303014287" f鈭�g4(b)g鈭�f2(c)f鈭�f1(d)g鈭�g0.

Short Answer

Step by step solution

Part (a) Step 1. Given Information.

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

Part (b) Step 1. Given Information.

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

Part (c) Step 1. Given Information.

Part (c) Evaluation of a functional value.

Part (d) Given Information.

Part (d) Evaluation of a functional value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Probability and Statistics

Pure Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find for the given functions $f, g$ such that
$f (x) = |x - 2|, g (x) = \frac{3}{x^{2} + 2}$ .
Find : (a)role="math" localid="1646303014287" $(f 鈭� g) (4)$ (b) $(g 鈭� f) (2)$ (c) $(f 鈭� f) (1)$ (d) $(g 鈭� g) (0)$ .