To find the inverse, we are going to replace f(x) by y as:
[tex]y=\sqrt{4x+5}[/tex]Then, we need to solve for x as:
[tex]\begin{gathered} y^2=4x+5 \\ y^2-5=4x \\ \frac{y^2-5}{4}=x \\ x=\frac{y^2-5}{4} \end{gathered}[/tex]Finally, we need to interchange y and x as:
[tex]y=\frac{x^2-5}{4}[/tex]Answer: the inverse of the function is:
[tex]y=f^{-1}(x)=\frac{x^2-5}{4}[/tex]