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Chapter 10: Q. 36 (page 1004)

In the following exercises, determine whether or not the given functions are inverses.
f(x)=5x-4andg(x)=x-45.

Short Answer

Expert verified

No, the given functions are not inverses of each other.

Step by step solution

01

Step 1. Given and explanation

We have f(x)=5x-4andg(x)=x-45.

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 means f(x-45).

Solving this gives us,

f(x-45)=x5(x-45)-4=xx-4-4=xx-8=x

This statement is not true.

03

Step 3. Final Answer

As we can see that f(g(x))=xis not true here, so these functions are not inverses of each other.

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