   Chapter 1, Problem 12P ### 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

# (a) Show that the function f ( x ) = ln ( x + x 2 + 1 ) is an odd function.(b) Find the inverse function of f.

(a)

To determine

To show: The function f(x)=ln(x+x2+1) is an odd function.

Explanation

Result used:

f is an odd function if and only if f(x)=f(x) for all x in the domain of f.

logab=logalogb

Proof:

Consider the function f(x)=ln(x+x2+1)

Substitute x=x in f(x).

f(x)=ln(x+(x)2+1)=ln(x+x2+1)

Rationalize the numerator,

f(x)=ln[(x+x2+1)(xx2+1xx2+1)

(b)

To determine

To find: The inverse function of f.

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