   Chapter 1, Problem 19RE ### 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

# If f(x) = In x and g(x) = x2 – 9. find the functions (a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘ g , and their domains.

(a)

To determine

To find: The function fg and its domain.

Explanation

Given:

The functions are f(x)=lnx,g(x)=x29.

Calculation:

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

(fg)(x)=f(g(x))=f(x29)

Substitute x29 for x in f(x),

f(x29)=ln(x29)

Thus, the composite function (fg)(x)=ln(x29)

(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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