Step-by-step explanation:
if I understand this correctly than you are looking for the inverse function of f(x) = y = 3x³.
the inverse function simply tries to calculate the original x it of the original y.
and then, to make it a formal function, we rename x to y and y to x.
y = 3x³
x³ = y/3
![x = \sqrt[3]{ \frac{y}{3} }](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7By%7D%7B3%7D%20%7D%20)
=> as "regular" function
![y = {f}^{ - 1} (x)= \sqrt[3]{ \frac{x}{3} }](https://tex.z-dn.net/?f=y%20%20%3D%20%20%7Bf%7D%5E%7B%20-%201%7D%20%28x%29%3D%20%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7Bx%7D%7B3%7D%20%7D%20)