Question

Let f(x) = (3x^3+17)^3 and g(x) = 3x^3 + 17. given that f(x) = (h*g)(x) find h(x)

Answer 1

We have that f(x) and g(x) are defined as:

`\begin{gathered} f(x)=(3x^3+17)^3 \\ g(x)=3x^3+17 \end{gathered}`

If f(x) is also related to h(x) and g(x) as:

`f(x)=(h\cdot g)(x)`

We can then find h(x) as:

`\begin{gathered} f(x)=h(x)\cdot g(x) \\ h(x)=(f(x))/(g(x)) \end{gathered}`

If we replace f(x) and g(x) we obtain:

`h(x)=(f(x))/(g(x))=((3x^3+17)^3)/(3x^3+17)=(3x^3+17)^2`

Answer: h(x) = (3x^3 + 17)^2