Composite Functions
Given the functions:
[tex]\begin{gathered} f(x)=3x^2+4 \\ g(x)=3x-2 \end{gathered}[/tex]
It's required to find the composition of g and f (g o f)(x).
The composition of g and f is equivalent to substituting f(x) into g(x) as follows:
[tex](g\circ f)(x)=3(3x^2+4)-2[/tex]
Operating:
[tex]\begin{gathered} (g\circ f)(x)=9x^2+12-2 \\ Simplifying: \\ (g\circ f)(x)=9x^2+10 \end{gathered}[/tex]
