Q. 3 In Problems 2 鈥� 4, for the giv... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 3 (page 343)

In Problems 2 鈥� 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = \sqrt{x + 2} : g (x) = 2 x^{2} + 1$

Short Answer

Expert verified

$(a) (f o g) (2) = \sqrt{11} (b) (g o f) (- 2) = 1 (c) (f o f) (4) = \sqrt{\sqrt{6} + 2} (d) (g o g) (- 1) = 19$

Step by step solution

Part (a) Step 1: Given information

WE are given with two functions f(x) and g(x)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1$

Part(a) : Step 2:Calculate (f o g)(2)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (f o g) (2) = f (g (2) g (2) = 2 {(2)}^{2} + 1 = 9 f (9) = \sqrt{9 + 2} = \sqrt{11} (f o g) (2) = \sqrt{11}$

Part(b): Step 1: Calculate (g o f) (-2)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (g o f) (- 2) = g (f (- 2)) f (- 2) = \sqrt{- 2 + 2} = 0 g (0) = 2 {(0)}^{2} + 1 = 1 (g o f) (- 2) = 1$

Part(c) : Step 1: (f o f)(4)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (f o f) (4) = f (f (4)) f (4) = \sqrt{4 + 2} = \sqrt{6} f (\sqrt{6}) = \sqrt{\sqrt{6} + 2} (f o f) (4) = \sqrt{\sqrt{6} + 2}$

Part(d): Step 1: ( g o g) (-1)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (g o g) (- 1) = g (g (- 1)) g (- 1) = 2 {(- 1)}^{2} + 1 = 3 g (3) = 2 {(3)}^{2} + 1 = 19$

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91影视

In Problems 2 鈥� 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = \sqrt{x + 2} : g (x) = 2 x^{2} + 1$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part(a) : Step 2:Calculate (f o g)(2)

Part(b): Step 1: Calculate (g o f) (-2)

Part(c) : Step 1: (f o f)(4)

Part(d): Step 1: ( g o g) (-1)

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91影视

In Problems 2 鈥� 4, for the given functions f and g find:(a) (f o g)(2)(b) (g o f) (-2)(c) (f o f)(4)(d) ( g o g) (-1)f(x)=x+2:g(x)=2x2+1

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part(a) : Step 2:Calculate (f o g)(2)

Part(b): Step 1: Calculate (g o f) (-2)

Part(c) : Step 1: (f o f)(4)

Part(d): Step 1: ( g o g) (-1)

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Logic and Functions

Decision Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 2 鈥� 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = \sqrt{x + 2} : g (x) = 2 x^{2} + 1$