Find the Inverse f(x)=((x+3)^(1/3))/8

Rewrite the equation as ${\displaystyle \frac{{(y+3)}^{\frac{1}{3}}}{8}=x}$.

Multiply both sides of the equation by ${\displaystyle 8}$.

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.

Subtract ${\displaystyle 3}$ from both sides of the equation.

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 ${\displaystyle f^{-1}\left(x\right)=512x^3-3}$ is the inverse of ${\displaystyle f\left(x\right)=\frac{{(x+3)}^{\frac{1}{3}}}{8}}$.