3. Find the inverse of the function f(x)=sqrt (x-2)

To find the inverse of the function $f(x)=\sqrt{x-2}$, we need to follow these steps:<br /><br />1. Replace $f(x)$ with $y$: $y=\sqrt{x-2}$<br /><br />2. Swap $x$ and $y$: $x=\sqrt{y-2}$<br /><br />3. Solve for $y$:<br /> - Square both sides: $x^2=y-2$<br /> - Add 2 to both sides: $y=x^2+2$<br /><br />Therefore, the inverse function is $f^{-1}(x)=x^2+2$.