   Chapter 1.3, Problem 37E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the functions (a) f ◦ g, (b) g ◦ f, (c) f ◦ f, and (d) g ◦ g and their domains.37. f ( x ) = x + 1 x , g ( x ) = x + 1 x + 2

(a)

To determine

To find: The function fg and its domain.

Explanation

Given:

The functions are f(x)=x+1x,g(x)=x+1x+2 .

Calculation:

The composite function (fg)(x) is defined as follows.

(fg)(x)=f(g(x))=f(x+1x+2)

Substitute x+1x+2 for x in f(x) .

f(x+1x+2)=x+1x+2+1x+1x+2=x+1x+2+x+2x

(b)

To determine

To find: The function gf and its domain.

(c)

To determine

To find: The function ff and its domain.

(d)

To determine

To find: The function gg and its domain.

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