Question

Using composition of functions, determine if the two functions are inverses of each other.

Answer 1

Neither of the two compositions is equal to x, so the correct option is A.

How to know if the functions are inverses?

We know that two functions f(x) and g(x) are inverses if:

$f(g(x)) = x\\\\g(f(x)) = x$

Here we have:

$f(x) = \sqrt{x} + 4\\ \\g(x) = x^2 - 4$

By using composition, we get:

$f(g(x)) = \sqrt{g(x)} + 4 = \sqrt{x^2 - 4} + 4\\\\g(f(x)) = (f(x))^2 - 4 = (\sqrt{x} + 4)^2 - 4$

Is immediate to notice that neither of these expressions are equal to x, so we can conclude that these two functions are not inverses. So the correct option is A.

If you want to learn more about inverse functions.

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