   Chapter 1.3, Problem 33E ### 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.33. f ( x ) = 3 x + 5 , g ( x ) = x 2 + x

(a)

To determine

To find: The function fg and its domain.

Explanation

Given:

The functions are f(x)=3x+5,g(x)=x2+x .

Calculation:

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

(fg)(x)=f(g(x))=f(x2+x)

Substitute x2+x for x in f(x) ,

(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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