For the function f(x)=frac{x^{frac{1}{3}}}{5}, find f^{-1}(x).

Question

Accepted Answer

Step:1 ：(f^{-1}(x)) is defined as the number (y) such that (f(y)=x). Thus, we solve the equation (frac{y^{frac{1}{3}}}{5} = x).Step:2 ：Multiplying both sides by 5, we have (y^{frac{1}{3}} = 5x).Step:3 ：Now, we raise both sides to the power of 3 to eliminate the cube root: ((y^{frac{1}{3}})^3 = (5x)^3).Step:4 ：This simplifies to (y = 125x^3).Step:5 ：So, the inverse function is (f^{-1}(x) = boxed{125x^3}).

Answer

Step: 1 ：(f^{-1}(x)) is defined as the number (y) such that (f(y)=x). Thus, we solve the equation (frac{y^{frac{1}{3}}}{5} = x).Step: 2 ：Multiplying both sides by 5, we have (y^{frac{1}{3}} = 5x).Step: 3 ：Now, we raise both sides to the power of 3 to eliminate the cube root: ((y^{frac{1}{3}})^3 = (5x)^3).Step: 4 ：This simplifies to (y = 125x^3).Step: 5 ：So, the inverse function is (f^{-1}(x) = boxed{125x^3}).

For the function $f (x) = \frac{x^{\frac{1}{3}}}{5}$ , find $f^{- 1} (x)$ .

Answer

Popular Problems

For the function f(x)=x135, find f−1(x).

Answer

Popular Problems

For the function $f (x) = \frac{x^{\frac{1}{3}}}{5}$ , find $f^{- 1} (x)$ .