# To express: The function u ( t ) = tan t 1 + tan t 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 46E
To determine

## To express: The function u(t)=tant1+tant in the form of (f∘g)(t).

Expert Solution

The function u(t)=tant1+tant can be expressed as u(t)=f(g(t)), where f(t)=t1+t and  g(t)=tant.

### Explanation of Solution

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.

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

Substitute tant for t in f(t).

f(tant)=tant1+tant=u(t)

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

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