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:

$\begin{gathered} f(x)=h(x)\cdot g(x) \\ h(x)=\frac{f(x)}{g(x)} \end{gathered}$

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

$h(x)=\frac{f(x)}{g(x)}=\frac{(3x^3+17)^3}{3x^3+17}=(3x^3+17)^2$

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