Find the Inverse f(x)=(x+8)^(1/5)

Rewrite the equation as ${\displaystyle {(y+8)}^{\frac{1}{5}}=x}$.

Raise each side of the equation to the power of ${\displaystyle 5}$ to eliminate the fractional exponent on the left side.

Simplify the left side.

Subtract ${\displaystyle 8}$ 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 ${\displaystyle f^{-1}\left(x\right)=x^5-8}$ is the inverse of ${\displaystyle f\left(x\right)={(x+8)}^{\frac{1}{5}}}$.