# To express: The function v ( t ) = sec ( t 2 ) tan ( t 2 ) in the form of ( f ∘ g ) ( t ) .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.3, Problem 45E
To determine

## To express: The function v(t)=sec(t2)tan(t2) in the form of (f∘g)(t) .

Expert Solution

The function v(t)=sec(t2)tan(t2) can be expressed as v(t)=f(g(t)) where f(t)=secttant and  g(t)=t2 .

### Explanation of Solution

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 .

Verification:

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

(fg)(t)=f(g(t))

Substitute t2 for x in f(t) .

f(t2)=sect2tant2=v(t)

Thus, it is verified 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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