Question

Let g(x) = 2x and h(x) = x^2 + 4. Find the value.(g o h) (0)a) 4b) 8c) 0d) 16

Answer 1

$\begin{gathered} \text{Given} \\ g(x)=2x \\ h(x)=x^2+4 \end{gathered}$

Solve for (g o h)(x)

$\begin{gathered} (g\circ f)(x)=g\big(f(x)\big) \\ (g\circ f)(x)=g(x^2+4) \\ (g\circ f)(x)=2(x^2+4) \\ (g\circ f)(x)=2x^2+8 \end{gathered}$

Next substitute x = 0

$\begin{gathered} (g\circ f)(x)=2x^2+8 \\ (g\circ f)(0)=2(0)^2+8 \\ (g\circ f)(0)=8 \end{gathered}$$\text{Therefore, }(g\circ f)(0)=8$