Explanation:
f(x) = y = 64x³ - 1
y + 1 = 64x³
(y + 1)/64 = x³
![x = \sqrt[3]{(y + 1) / 64}](https://img.qammunity.org/2023/formulas/mathematics/high-school/uc53kbm51hvqeq6twxzuai31fxm0cbvbkz.png)
![x = \sqrt[3]{y + 1} / 4](https://img.qammunity.org/2023/formulas/mathematics/high-school/unq4izu1gis190o9w8fl2sdav91otx9cqc.png)
that is the actual inverse function to calculate the original x value for a given y value of the original function.
but to make it a "normal" function, we need to rename the variables (x to y, y to x) :
![y = \sqrt[3]{x + 1} / 4](https://img.qammunity.org/2023/formulas/mathematics/high-school/cune4dus6akq4akuojdytg5ztd49osdjdm.png)
this is now f^-1(x)
but careful, don't get confused, if dealing together with the original function, this "x" is actually standing for the "y" of the original function ...