Find the Inverse f(x)=(x^(1/3))/4

Rewrite the equation as ${\displaystyle \frac{y^{\frac{1}{3}}}{4}=x}$.

Multiply both sides of the equation by ${\displaystyle 4}$.

Simplify the left side.

Raise each side of the equation to the power of ${\displaystyle 3}$ to eliminate the fractional exponent on the left side.

Simplify the exponent.

To verify the inverse, check if ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$.

Evaluate ${\displaystyle f^{-1}\left(f\left(x\right)\right)}$.

Evaluate ${\displaystyle f\left(f^{-1}\left(x\right)\right)}$.

Since ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$, then ${\displaystyle f^{-1}\left(x\right)=64x^3}$ is the inverse of ${\displaystyle f\left(x\right)=\frac{x^{\frac{1}{3}}}{4}}$.