Question

f(x)=3x+2;g(x)=x+2 ; find f(g(x))

Answer 1

We have the functions:

$f(x)=3x+2$

and

$g(x)=x+2$

and we need to find the composite function f(g(x)), to do this we plug the function g(x) instead of x in the function f(x), that is:

$\begin{gathered} f(g(x))=f(x+2) \\ =3(x+2)+2 \\ =3x+6+2 \\ =3x+8 \end{gathered}$

Therefore:

$f(g(x))=3x+8$