   Chapter 1.3, Problem 47E ### 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.47. v(t) = sec(t2) tan(t2)

To determine

To express: The function v(t)=sec(t2)tan(t2) in the form of (fg)(t) .

Explanation

Given:

The composite function is v(t)=sec(t2)tan(t2) .

Calculation:

Name the expression t2 as  g(t)=t2 .

Thus, v(t)=sec(g(t))tan(g(t))

It can be expressed as v(t)=f(g(t)), as v(t) is a composition of f and g.

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

Therefore, f(t)=secttant .

Hence, it can be concluded that v(t)=sec(t2)tan(t2) can be expressed as (fg)(t)=f(g(t)) where f(t)=secttant and  g(t)=t2

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