Chapter 11: Q. 37 (page 1069)

In the following exercises, determine whether or not the given functions are inverses.
$f (x) = \sqrt{x + 2} a n d g (x) = x^{2} - 2$

Short Answer

Expert verified

Yes, the given functions are inverses of each other.

Step by step solution

Step 1. Given and explanation.

We have $f (x) = \sqrt{x + 2} a n d g (x) = x^{2} - 2$ .

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 $f (x)$ .

So it means $f (x^{2} - 2)$ .
Solving this gives us,

localid="1667915007683" $f (x^{2} - 2) = x \sqrt{(x^{2} - 2) + 2} = x \sqrt{x^{2}} = x x = x$
Hence verified.

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

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

So it means $g (\sqrt{x + 2})$ .

Solving this gives us,

${(\sqrt{x + 2})}^{2} - 2 = x x + 2 - 2 = x x = x$
Hence verified.

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In the following exercises, determine whether or not the given functions are inverses.
$f (x) = \sqrt{x + 2} a n d g (x) = x^{2} - 2$

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+2andg(x)=x2-2

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

Decision Maths

Pure Maths

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Study anywhere. Anytime. Across all devices.

In the following exercises, determine whether or not the given functions are inverses.
$f (x) = \sqrt{x + 2} a n d g (x) = x^{2} - 2$