express the function f(x)= sin^3 x in the form g of f?

Question

I would like to know how do you determine which one is f(x) and which one is g(x).

Answer 1

It could be expressed in many ways. For example, if f(x)=x³  and   g(x)=sin(x), then f(g(x))=sin³(x). But g(f(x))≠f(g(x))

Alternatively, you can take f(x)=x, g(x)=sin³(x). Or it ccould be as  f(x)=x^3/2,  g(x)=sin²(x), etc.

Answer 2

f(x) = sin x

g(x) = x³

 

g o f(x) = (sin x)³, the same as sin²x