Answer:
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
[tex]\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}[/tex]
We would plot the graph of the inverse. It is shown below
