The answer is the first option, \(f\textsuperscript{-1}(x)=x^2+5; y \geq 5.\)
When finding the inverse of a function, first replace \(f(x)\) with \(y\), and interchange the variables.
\(f(x)= \sqrt{x-5} \\
y= \sqrt{x-5} \\
x= \sqrt{y-5}\)
Then, solve the equation for y. This will give you the inverse function.
\(x= \sqrt{y-5} \\ x^2 = y-5 \\ y = x^2+5 \\
f\textsuperscript{-1}(x)=x^2+5\)
