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Chapter 10: Q. 38 (page 1004)

In the following exercises, determine whether or not the given functions are inverses.
f(x)=x-43andg(x)=x3+4

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-43andg(x)=x3+4.

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 this means f(x3+4).

Solving this will give us,

f(x3+4)=x(x3+4)-43=xx33=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(x-43).

Solving it will give us,

g(x-43)=x(x-43)3+4=xx-4+4=xx=x
Hence verified.

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