Composition of functions

Question

f(x)=3-2x

g(x)= x²-2x-9

Find (f o g(3)) and (g o f(3))

Answer 1

f(x) = 3-2x

g(x) = x^2 -2x - 9

find (fog)(x) = f(g(x)) = f(x^2 -2x -9)= 3 - 2(x^2 -2x -9) = 3 -2x^2 +4x +18= 21 -2x^2 +4x

(fog)(3) = 21 -2(3)^2 +4(3) = 21-18+12 = 15

(gof)(x) = g(f(x)) = g(3-2x) = (3-2x)^2 -2(3-2x) - 9= 9 -12x +4x^2 -6 +4x -9= 4x^2 -8x -6

(fof)(3) 4(3^2) -8(3) -6 = 36-24-6 = 6

or

do the x=3 from the start

f(3) = 3-2x = -3

g(3) = 9-6 -9=-6

f(g(3)) = 3-2(-6) = 15

g(f(3) = (-3)^2 -2(-3) -9 = 6

Answer 2