on f(x)=frac{x}{3}+10, find f^{-1}(x)

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Step:1 ：Given the function (f(x)=frac{x}{3}+10), we want 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 in the original function and then solve for y.Step:3 ：Replace (f(x)) with x in the function (f(x) = frac{x}{3} + 10), we get (x = frac{y}{3} + 10).Step:4 ：Solving for y, we get (y = 3x - 30).Step:5 ：Therefore, the inverse function of (f(x)=frac{x}{3}+10) is (f^{-1}(x)=3x-30).Step:6 ：Final Answer: (f^{-1}(x)=boxed{3x-30})

Answer

Step: 1 ：Given the function (f(x)=frac{x}{3}+10), we want 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 in the original function and then solve for y.Step: 3 ：Replace (f(x)) with x in the function (f(x) = frac{x}{3} + 10), we get (x = frac{y}{3} + 10).Step: 4 ：Solving for y, we get (y = 3x - 30).Step: 5 ：Therefore, the inverse function of (f(x)=frac{x}{3}+10) is (f^{-1}(x)=3x-30).Step: 6 ：Final Answer: (f^{-1}(x)=boxed{3x-30})

on $f(x)=\frac{x}{3}+10$, find $f^{-1}(x)$

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