Question

For f(x)=3x-4 and g(x)=4x^2-3What is (g o f)(x) =?

Answer 1

Given:

The functions

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

Required:

$\text{ What is }(g\circ f)(x)?$

Explanation:

The solution steps are:

$\begin{gathered} g\circ f(x)=g(f(x)) \\ g(f(x))=g(3x-4) \\ g(3x-4)=4(3x-4)^2-3 \\ =4(9x^2+16-24x)-3 \\ =36x^2+64-96x-3 \\ =36x^2-96x+61 \end{gathered}$

Answer:

$(g\circ f)(x)=36x^2-96x+61$