Question

how do I find the inverse of this function? a. y=2(x-1)^3

Answer 1

The inverse of the function is;

$\frac{\sqrt[3]{x\text{ }}\text{ +2}}{2}$

Here, we want to find the inverse of the given function

We start by making x the subject of the formula

We have this as follows;

$\begin{gathered} y=2(x-1)^3 \\ \sqrt[3]{y\text{ }}\text{ = 2(x-1)} \\ \sqrt[3]{y}\text{ = 2x - 2} \\ \sqrt[3]{y}\text{ + 2 = 2x} \\ \\ x\text{ = }\frac{\sqrt[3]{y}\text{ + 2}}{2} \end{gathered}$

Now, we replace the y in the inverse equation with x

Thus, we have the inverse as;

$\frac{\sqrt[3]{x\text{ }}\text{ +2}}{2}$