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Chapter 5: Q 55. (page 257)

In Problems 53鈥�58, find functionsf and g so that f鈭�g=H.

H(x)=x2+1

Short Answer

Expert verified

The required functions aref(x)=x;g(x)=x2+1.

Step by step solution

01

Step 1. Given information. 

The given function is:

H(x)=x2+1

In the given function H takes x2+1and raises to the power 12.

Now decompose H by raising g(x)=x2+1to the power 12.

Let's take g(x)=x2+1and f(x)=2.

02

Step 2. Find f∘g.

(f鈭�g)(x)=f(g(x))

Substitute g(x)=x2+1in the function f(g(x)),

Then the function will becomef(x2+1).

Now replace x with x2+1in f(x)=x,

f(x2+1)=x2+1x2+1=H(x)

As we can see that f鈭�g=H, therefore the values of the function that we assumed are correct.

f(x)=x;g(x)=x2+1

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