To answer this question, first, we set the following equation:
[tex]y=(x-5)^2,[/tex]and solve it for x.
Taking the square root, we get:
[tex]\sqrt[]{y}=x-5.[/tex]Adding 5 to both sides of the equation, we get:
[tex]\sqrt[]{y}+5=x.[/tex]Now, we exchange x for y:
[tex]y=\sqrt[]{x}+5.[/tex]Therefore:
[tex]f^{-1}(x)=\sqrt[]{x}+5.[/tex]Answer:
[tex]f^{-1}(x)=\sqrt[]{x}+5.[/tex]