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Chapter 5: Q 57. (page 257)

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

H(x)=2x+1

Short Answer

Expert verified

The required functions aref(x)=x;g(x)=2x+1.

Step by step solution

01

Step 1. Given information.

The given function is:

H(x)=2x+1

In the given function H takes 2x+1and takes the absolute value of the function.

Now decompose H by taking the absolute value of the function.

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

02

Step 2. Find f∘g.

(f鈭�g)(x)=f(g(x))

Substituteg(x)=2x+1in the function f(g(x)),

Then the function will become f(2x+1).

Now replace x with 2x+1in f(x)=x,

f(2x+1)=2x+12x+1=H(x)

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

f(x)=x;g(x)=2x+1

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