Q. 7 In Problems 5鈥�7, find f o g, g... [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. 7 (page 348)

In Problems 5鈥�7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.
$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x}$

Short Answer

Expert verified

$(f o g) (x) = \frac{1 + x}{1 - x} D o m a i n : {x | x 鈮� 0, x 鈮� 1} (g o f) (x) = \frac{x - 1}{x + 1} D o m a i n : {x | x 鈮� - 1, x 鈮� 1} (f o f) (x) = x d o m a i n : {x | x 鈮� 1} (g o g) (x) = x d o m a i n : {x | x 鈮� 0}$

Step by step solution

Given information

we are given with two functions

$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x}$

Part(a) : Step 1:Composition and domain

$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x} (f o g) (x) = f (g (x)) = f (\frac{1}{x}) = \frac{\frac{1}{x} + 1}{\frac{1}{x} - 1} = \frac{1 + x}{1 - x} D o m a i n " {x | x 鈮� 0, x 鈮� 1}$

Part(b): Step 1 :Composition and domain

$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x} (g o f) (x) = g (f (x)) = g (\frac{x + 1}{x - 1}) = \frac{1}{\frac{x + 1}{x - 1}} = \frac{x + 1}{x - 1} D o m a i n " {x | x 鈮� - 1, x 鈮� 1}$

Part(c) : Step 1:Composition and domain

$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x} (f o f) (x) = f (f (x)) = f (\frac{x + 1}{x - 1}) = \frac{\frac{x + 1}{x - 1} + 1}{\frac{x + 1}{x - 1} - 1} = x D o m a i n : {x | x 鈮� 1}$

Part(d) : Step 1: Composition and domain

$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x} (g o g) (x) = g (g (x)) = g (\frac{1}{x}) = \frac{1}{\frac{1}{x}} = x D o m a i n : {x | x 鈮� 0}$

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91影视

In Problems 5鈥�7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.
$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x}$

Short Answer

Step by step solution

Given information

Part(a) : Step 1:Composition and domain

Part(b): Step 1 :Composition and domain

Part(c) : Step 1:Composition and domain

Part(d) : Step 1: Composition and domain

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91影视

In Problems 5鈥�7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function. f(x)=x+1x-1g(x)=1x

Short Answer

Step by step solution

Given information

Part(a) : Step 1:Composition and domain

Part(b): Step 1 :Composition and domain

Part(c) : Step 1:Composition and domain

Part(d) : Step 1: Composition and domain

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

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Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 5鈥�7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.
$f (x) = \frac{x + 1}{x - 1} g (x) = \frac{1}{x}$