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Chapter 10: Q. 35 (page 1004)

In the following exercises, determine whether or not the given functions are inverses.
f(x)=7x+3andg(x)=x-37

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)=7x+3andg(x)=x-37.

We know that if functions are inverse of each other, sof(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 this meansf(x-37).
Solving this will give us,

role="math" localid="1644922078076" f(x-37)=x7(x-37)+3=xx-3+3=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 this means g(7x+3).

Solving it gives us,

g(7x+3)=x(7x+3)-37=x7x7=xx=x
Hence verified.

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