Question

I’m learning about compositions of. Functions and I want to know how I can solve these equations

Answer 1

1a)

We want to find h(g(18))

The first step is to find h(g(x). To do this, we would substitute x = g(x) into h(x). We have

$\begin{gathered} h(g(x))\text{ = }(\sqrt[]{x\text{ - 2}})^2\text{ }+\text{ 11} \\ \text{The square cancels the square root. It becomes} \\ h(g(x))\text{ = x - 2 + 11} \\ h(g(x))\text{ = x + 9} \end{gathered}$

To find h(g(18)), we would substitute x = 18 into h(gx)). We have

h(g(18)) = 18 + 9

h(g(18)) = 27