$f(x)=x^{\frac{1}{3}}+2$, find $f^{-1}(x)$

Step 1 ：Given the function \(f(x)=x^{\frac{1}{3}}+2\), we need to find the inverse function \(f^{-1}(x)\).

Step 2 ：To find the inverse of a function, we switch the roles of x and y (or f(x)) and solve for y. In this case, we need to solve the equation \(x = y^{\frac{1}{3}} + 2\) for y.

Step 3 ：Solving the equation gives us the inverse function as \(f^{-1}(x) = 8.0*(0.5*x - 1)^3\). However, this is not in its simplest form.

Step 4 ：We can simplify this to \(f^{-1}(x) = 8*(x/2 - 1)^3\).

Step 5 ：Final Answer: \(f^{-1}(x) = \boxed{8*(x/2 - 1)^3}\)