Find the inverse of the function. \[ f(x)=\sqrt{x-4} \]

Find the inverse of the function \( f(x)=\sqrt{x-4} \) Function by following steps: - step0: Find the inverse: \(f\left(x\right)=\sqrt{x-4}\) - step1: Replace \(f\left(x\right)\) with \(y:\) \(y=\sqrt{x-4}\) - step2: Interchange the variables: \(x=\sqrt{y-4}\) - step3: Swap the sides: \(\sqrt{y-4}=x\) - step4: Raise both sides to the \(2\)-th power\(:\) \(\left(\sqrt{y-4}\right)^{2}=x^{2}\) - step5: Evaluate the power: \(y-4=x^{2}\) - step6: Move the constant to the right side: \(y=x^{2}+4\) - step7: Replace \(y\) with \(f^{-1}\left(x\right):\) \(f^{-1}\left(x\right) = x^{2}+4\) The inverse of the function \( f(x)=\sqrt{x-4} \) is given by \( f^{-1}(x) = x^{2}+4 \).