HELP please with this question!?

Question

Let h(x) = (x^3 – 2)^4 + 2(x^3 – 2). Deterime two functions f and g such that h(x) = (f follows g)(x)

a) f(x) = x^4 + 2x and g(x) = x^3 – 2
b) f(x) = x^4 + 2 and g(x) = x^3 – 2
c) f(x) = x^3 – 2 and g(x) = x^4 +2x
d) f(x) = (x^3 – 2)^4 + 2 and g(x) = x^3 – 2

Answer 1

the answer is a, because when you plug (x^3 - 2) in for x in f(x), you get h(x). that's exactly what happens when you compose two functions.

Answer 2

Given h(x)=(x^3-2)^4 + 2(x^3-2)
By trial and error method First let us take (a)
therefore
(f follows g)=f(g(x)
=>fog(x)=f(x^3-2)
=>fog(x)=(x^3-2)^4+2(x^3-2)=h(x)
Thus f(x) and g(x) hold the functions as in equ (a)

Answer 3

h(x) = f( g(x)) if f(x) = x^4 + 2x and g(x) = x^3 - 2.

however you name them, x^3 - 2 must be the inner function and x^4 + 2x must be the outer.