Need help with composite function?

Question

Find the rules for the composite functions f o g and g o f. 
f(x)=8x^2+6x+5; g(x)=x+2
 

Answer 1

f(x)=8x^2+6x+5; g(x)=x+2

To find  (g o f)(x)

= g [ f(x) ]

= g [8x^2+6x+5]

= [8x^2+6x+5] +2

= 8x^2+6x+ 7.

To find  ( f o g)(x)

= f [ g(x) ]

= f [ x+2]

= 8(x+2)^2 + 6(x+2) + 5

( formula : (a + b)^2 = a^2 + 2(a)(b) +b^2 )

= 8(x^2+2((2)(x))+2^2) + 6x + 12 + 5

= 8(x^2+4x+4) +6x + 17

= 8x^2 +32x + 32 + 6x +17

= 8x^2 + 38x + 49.

The solution's are (f o g) = 8x^2 + 38x + 49 , (g o f) = 8x^2+6x+ 7.