Find the composite function

Let f(x) = 8x^2 + 5 and g(x) = x – 2.
Find the composite function ( f o g)(x) and simplify, and Find ( f o g )(−1)

Solution:

We evaluate composite functions by substitution: 


(fog)(x) =f(g(x))= 8(x-2)^2 + 5 


and then we simplify... 


(fog)(x) = 8(x^2-4x+4)+5=8x^2-32x+37 

at x=-1 we get: 
8(-1)^2-32(-1)+37=77