Question

g(x) = 3x - 4h(x) = x^2 + 1Find g(h(x))

Answer 1

Given the functions below

$\begin{gathered} g(x)=3x-4 \\ h(x)=x^2+1 \end{gathered}$

To find the composite function g(h(x)), we will substitute the whole of h(x) as x in the function g(x). This process can be done below

$\begin{gathered} g(h(x))=3(hx)-4_{} \\ \text{ Since}h(x)=x^2+1 \\ g(h(x))=3(x^2+1)-4 \end{gathered}$

Simplify the equation above using distributive property of algebra

$\begin{gathered} g(h(x))=3(x^2)+3(1)-4 \\ =3x^2+3-4 \\ =3x^2-1 \end{gathered}$

Hence, the composite function g(h(x)) is

$3x^2-1$