Q. 4 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. 4 (page 348)

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)
$f (x) = e^{x} g (x) = 3 x - 2$

Short Answer

Expert verified

$(a) (f o g) (2) = e^{4} (b) (g o f) (- 2) = 3 e^{- 2} - 2 (c) (f o f) (4) = e^{e^{4}} (d) (g o g) (- 1) = - 17$

Step by step solution

Part(a) Step 1: Given Information

We are given with two functions

$f (x) = e^{x} g (x) = 3 x - 2$

Part(a) : Step 2: Composition of functions

$f (x) = e^{x} g (x) = 3 x - 2 (f o g) (2) = f (g (2)) g (2) = 3 (2) - 2 = 4 f (4) = e^{4} (f o g) (2) = e^{4}$

Part(b) : Step 1: composition of functions

$f (x) = e^{x} g (x) = 3 x - 2 (g o f) (- 2) = g (f (- 2)) f (- 2) = e^{- 2} g (e^{- 2}) = 3 e^{- 2} - 2 (g o f) (- 2) = 3 e^{- 2} - 2$

Part(c): Step 1: composition of functions

$f (x) = e^{x} g (x) = 3 x - 2 (f o f) (4) = f (f (4)) f (4) = e^{4} f (e^{4}) = e^{e^{4}} (f o f) (4) = e^{e^{4}}$

Part (d) : Step 1: composition of funcitons

$f (x) = e^{x} g (x) = 3 x - 2 (g o g) (- 1) = g (g (- 1) g (- 1) = 3 (- 1) - 2 = - 5 g (- 5) = 3 (- 5) - 2 = - 17 (g o g) (- 1) = - 17$

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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)
$f (x) = e^{x} g (x) = 3 x - 2$

Short Answer

Step by step solution

Part(a) Step 1: Given Information

Part(a) : Step 2: Composition of functions

Part(b) : Step 1: composition of functions

Part(c): Step 1: composition of functions

Part (d) : Step 1: composition of funcitons

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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)=exg(x)=3x-2

Short Answer

Step by step solution

Part(a) Step 1: Given Information

Part(a) : Step 2: Composition of functions

Part(b) : Step 1: composition of functions

Part(c): Step 1: composition of functions

Part (d) : Step 1: composition of funcitons

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Calculus

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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)
$f (x) = e^{x} g (x) = 3 x - 2$