39. What is the inverse of $f(x)=\sqrt{x+2}$ ?

Step 1 ：Let's denote the inverse of \(f(x)\) as \(g(x)\). So we can evaluate \(f\) at \(g(x)\) to get \(f(g(x))=\sqrt{g(x)+2}\).

Step 2 ：Since \(g\) is the inverse to \(f\), the left side is \(x\), so we have \(x=\sqrt{g(x)+2}\).

Step 3 ：To solve for \(g(x)\), we square both sides of the equation to get rid of the square root. This gives us \(x^2=g(x)+2\).

Step 4 ：Subtract 2 from both sides to isolate \(g(x)\), we find \(g(x) = \boxed{x^2-2}\).