Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 13 (page 256)

Find for the given functions $f, g$
$f (x) = 4 x^{2} - 3, g (x) = 3 - \frac{1}{2} x^{2}$ .
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) 97 (b) $\frac{- 163}{2}$ (c) 1 (d) $- \frac{3}{2}$ .

Step by step solution

Part (a) Step 1. Given Information.

The given functions are

$f (x) = 4 x^{2} - 3, g (x) = 3 - \frac{1}{2} x^{2}$ .

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

The functional valuee is :

(a) $(f 鈭� g) (4) = f (g (4)) = f (- 5) = 100 - 3 = 97$ .

Part (b) Step 1. Given Information.

The given function is

$f (x) = 4 x^{2} - 3, g (x) = 3 - \frac{1}{2} x^{2}$ .

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

The value of a function is

$(g 鈭� f) (2) = g (f (2)) = g (13) = 3 - \frac{169}{2} = - \frac{163}{2}$ .

Part (c) Step 1. Given Information.

The value of the function is

$f (x) = 4 x^{2} - 3, g (x) = 3 - \frac{1}{2} x^{2}$ .

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

The value of the function is

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

Part (d) Step 1. Given Infoormation.

The given function is

$f (x) = 4 x^{2} - 3, g (x) = 3 - \frac{1}{2} x^{2}$ .

Step 2. Evaluation of a functional value.

The value of the function is

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

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91影视

Find for the given functions $f, g$
$f (x) = 4 x^{2} - 3, g (x) = 3 - \frac{1}{2} x^{2}$ .
Find (a) $(f 鈭� g) (4)$ (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) Step 2. Evaluation of a functional value.

Part (d) Step 1. Given Infoormation.

Step 2. Evaluation of a functional value.

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91影视

Find for the given functionsf,gfx=4x2-3,g(x)=3-12x2.Find (a)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) Step 2. Evaluation of a functional value.

Part (d) Step 1. Given Infoormation.

Step 2. Evaluation of a functional value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

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