Question

X + 2Let g(x) = x2 + 2 and h(x) =5Evaluate (hog)(x).(h o g)(x) =(Simplify your answer.)

Answer 1

If we have two funcions, f(x) and g(x), fog is f(g(x)). In other words, we substitute the x in the first function for g(x).

In your question:

$\begin{gathered} g(x)=x^2+2 \\ h(x)=\frac{x+2}{5} \end{gathered}$

hog(x) = h(g(x))

$\begin{gathered} h(x)=\frac{x+2}{5} \\ hog(x)=h(g(x))=\frac{g(x)+2}{5} \\ hog(x)=\frac{(x^2+2)+2}{5} \\ hog(x)=\frac{x^2+4}{5} \\ \end{gathered}$