Let f RR be given by fxX2 4x and let g RR be given by gx8 x3

Let f: R->R be given by f(x)=X^2 +4x and let g: R->R be given by g(x)=8- x^3. Find and simplify f ?g(x) and g ?f(x).

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

fog(x) = f(g(x) :
f(8 - x^3)

(8 - x^3)^2 + 4(8 - x^3)

64 - 16x^3 + x^6 + 32 - 4x^3

x^6 - 20x^3 + 96 ---> ANSWER

gof(x) :
g(f(x))
g(x^2 + 4x)

8 - (x^2 + 4x)^3

8 - (x^6 + 12x^5 + 48x^4 + 64x^3)

-x^6 - 12x^5 - 48x^4 - 64x^3 + 8 ---> ANSWER