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Chapter 11: Q. 37 (page 1069)

In the following exercises, determine whether or not the given functions are inverses.
f(x)=x+2andg(x)=x2-2

Short Answer

Expert verified

Yes, the given functions are inverses of each other.

Step by step solution

01

Step 1. Given and explanation.

We have f(x)=x+2andg(x)=x2-2.

We know that if functions are inverse of each other, so f(g(x))=xandg(f(x))=x.

So by verifying this, we will check whether they are inverse of each other or not.

02

Step 2. Verifying f(g(x))=x

Here, we need to put value of g(x)in place of xin f(x).

So it meansf(x2-2).
Solving this gives us,

localid="1667915007683" f(x2-2)=x(x2-2)+2=xx2=xx=x
Hence verified.

03

Step 3. Verifying g(f(x))=x

Here, we need to put value of f(x)in place of xin g(x).

So it means g(x+2).

Solving this gives us,

(x+2)2-2=xx+2-2=xx=x
Hence verified.

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