### Home > CCA2 > Chapter 5 > Lesson 5.2.5 > Problem5-112

5-112.

If $f ( x ) = \sqrt { 7 - x } - 6$ and $g(x)=−(x+6)^2+7$ for $x\ge−6$, find $f(g(x))$ and $g(f(x))$. What do the results tell you about $f(x)$ and $g(x)$?

Substitute $-(x+6)^2+7\text{ }$ into $\sqrt{7-x}-6$ to find $f(g(x))$.

It should look like $f(g(x))=\sqrt{7-(-(x+6)^2+7)}-6.$

Substitute $\sqrt{7-x}-6$ into $-(x+6)^2+7$ to find $g(f(x))$.

$f(g(x))=g(f(x))=x$.
They are inverses.

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