Chapter 10: Q. 31 (page 1004)

In the following exercises, determine whether or not the given functions are inverses.
$f (x) = x + 8 a n d g (x) = x - 8$

Short Answer

Expert verified

Yes, the given functions are inverses of each other.

Step by step solution

Step 1. Given and explanation.

We have $f (x) = x + 8 a n d g (x) = x - 8$ .

We know that if functions are inverse of each other, so $f (g (x)) = x a n d g (f (x)) = x$ .

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

Step 2. Verifying f(g(x))=x

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

So this means $f (x - 8)$ .

Solving it will give us,
$f (x - 8) = x [(x - 8) + 8] = x x - 8 + 8 = x x = x$

Hence verified.

Step 3. Verifying g(f(x))=x.

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

So this means $g (x + 8)$ .

Solving it will give us,
$g (x + 8) = x [(x + 8) - 8] = x x + 8 - 8 = x x = x$
Hence verified.

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In the following exercises, determine whether or not the given functions are inverses.
$f (x) = x + 8 a n d g (x) = x - 8$

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Verifying f(g(x))=x

Step 3. Verifying g(f(x))=x.

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In the following exercises, determine whether or not the given functions are inverses.f(x)=x+8andg(x)=x-8

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Verifying f(g(x))=x

Step 3. Verifying g(f(x))=x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, determine whether or not the given functions are inverses.
$f (x) = x + 8 a n d g (x) = x - 8$