Given that f(x)=4x+3 and g(x)=8-x^2, calculate

Question

a) f(g(0))=

b) g(f(0))=

Answer 1

f(g(x)) = 4(8 - x^2) +3 = 32 - 4x^2 + 3 = -4x^2 + 35

g(f(x)) = 8 - (4x+3)^2 = 8 - (16x^2 + 24x + 9)

= 8 - 16x^2 - 24x - 9

= -16x^2 - 24x - 1

f(g(0)) = 35

g(f(0)) = -1

Now f(0) = 3 --> g(3) = 8 - 3^2 = 8-9 = -1 so g(f(0)) = g(3) = -1 which agrees

g(0) = 8 ---> f(8) = 35, so f(g(0)) = f(8) = 35 which agrees

the answers above in bold are checked, verified, and correct