What’s the function

Question

If g°h(x) = (2x-2)³, then the function could be ?

Answer 1

Mallory,

I believe that you need to find 2 functions, h(x) and g(x), so the composition of these two, g°h(x) = (2x-2)³ .

Please remember that x is the input, which enters into h(x) first, so it is the "inside" function, and the output will enter g(x), which is the outside function, to give you the final result.

By observation, you imagine that:

x----> h(x)=2x-2 ---> g(x)= x³ will result in (2x-2)³ , since what you need to do is replace the x in g(x) with the output of h(x), which is 2x-2.

So the answer is h(x)=2x-2 and g(x)= x³ _.

Answer 2

If (g o h)(x) = g(h(x)) = (2x-2)³ then h(x) = 2x-2 and g(x) = x³ would be possible choices for h(x) and g(x).