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

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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})

Answer

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})

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

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