BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 1.3, Problem 44E
To determine

To express: The function G(x)=x1+x3 in the form of (fg)(x) .

Expert Solution

Answer to Problem 44E

The function G(x)=x1+x3 can be expressed as G(x)=f(g(x)),  where f(x)=x3 and  g(x)=x1+x .

Explanation of Solution

The given composite function is G(x)=x1+x3 .

Name the expression x1+x as  g(x)=x1+x .

Thus, F(x)=g(x)3

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

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

Therefore, f(x)=x3 .

Hence, it can be concluded that G(x)=x1+x3 can be expressed as G(x)=f(g(x)), where f(x)=x3 and  g(x)=x1+x .

Verification:

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

(fg)(x)=f(g(x))

Substitute x1+x for x in f(x) .

f(x1+x)=x1+x3=G(x)

Thus, it is verified that G(x)=x1+x3 can be expressed as G(x)=f(g(x)),  where f(x)=x3 and  g(x)=x1+x .

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