Question

Graph the inverse of the function, f(x) = (x-2)^3 - 3

Answer 1

Step-by-step explanation:

The given function is expressed as

f(x) = (x-2)^3 - 3

We would find the inverse of the function. The first step is to replace f(x) with y and solve for y. It becomes

x = (y - 2)^3 - 3

x + 3 = (y - 2)^3

Taking the cube root of both sides

`\begin{gathered} \sqrt[3]{x\text{ + 3}}\text{ = y - 2} \\ y\text{ = = 2 +}\sqrt[3]{x\text{ + 3}} \\ Replacing\text{ y with f}^(-1)(x\text{ \rparen,} \\ f^(-1)(x)\text{ = 2 + }\sqrt[3]{x\text{ + 3}} \end{gathered}`

We would plot the graph of the inverse. It is shown below