Question

f(x) = V2 - 1 and h(x) = x² + 5Answer three questions about these functions.What is the value of f(h(2))?f(h(2)) =What is the value of h(f (16))?h(f(16)) =Based only on the previous compositions, is it possible that f and h are inverses?Choose 1 answer:YesBNo

Answer 1

Given:

$\begin{gathered} f(x)=\sqrt[]{x}-1 \\ h(x)=x^2+5 \end{gathered}$

To find: f(h(2))

So, we get,

$\begin{gathered} f(h(2))=f(2^2+5) \\ =f(9) \\ =\sqrt[]{9}-1 \\ =3-1 \\ =2 \end{gathered}$

Hence, the answer is, f(h(2))=2.

To find: h(f(16))

So, we get

$\begin{gathered} h(f(16))=h(\sqrt[]{16}-1) \\ =h(3) \\ =3^2+5 \\ =14 \end{gathered}$

Hence, the answer is, h(f(16))=14.

Since, h(f(16))=14

And, f and h are not inverses.