   Chapter 1.3, Problem 48E ### 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

# Express the function in the form f ◦ g.48. u ( t ) = tan t 1 + tan t

To determine

To express: The function u(t)=tant1+tant in the form of (fg)(t).

Explanation

Name the expression tant as  g(t)=tant.

Thus, u(t)=g(t)1+g(t).

Replace g(t) by t to obtain the expression for f(t).

Therefore, f(t)=t1+t.

Hence, it can be concluded that u(t)=tant1+tant can be expressed as (fg)(t)=f(g(t)) where f(t)=t1+t and  g(t)=tant.

Verification:

The composite function (fg)(t) is defined as follows

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