Question For the function f(x)=5x^(1)/(5)+3 , find f^-1(x) Answer f^-1(x)=(x^5-3)/(5) f^-1(x)=(} x 5-3 f^-1(x)=(x^5)/(5)-3 f^-1(x)=((x-3)/(5))^5

To find the inverse of the function $f(x)=5x^{\frac {1}{5}}+3$, we need to follow these steps:<br /><br />1. Replace $f(x)$ with $y$: $y=5x^{\frac {1}{5}}+3$<br />2. Swap $x$ and $y$: $x=5y^{\frac {1}{5}}+3$<br />3. Solve for $y$:<br /> - Subtract 3 from both sides: $x-3=5y^{\frac {1}{5}}$<br /> - Divide both sides by 5: $\frac {x-3}{5}=y^{\frac {1}{5}}$<br /> - Raise both sides to the power of 5: $\left(\frac {x-3}{5}\right)^5=y$<br /><br />Therefore, the inverse function is $f^{-1}(x)=\left(\frac {x-3}{5}\right)^5$.