Question

What is the inverse of function f?
f(x) = 64x3 - 1

Answer 1

Explanation:

f(x) = y = 64x³ - 1

y + 1 = 64x³

(y + 1)/64 = x³

`x = \sqrt[3]{(y + 1) / 64}`

`x = \sqrt[3]{y + 1} / 4`

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`

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 ...