[tex]f(x) = x^{2} - 25
[/tex] can be written as [tex]y = x^{2} - 25[/tex]
when finding inverse the first step is to interchange x and y in the equation
∴ [tex](x) = (y)^{2} - 25[/tex]
then you simply solve for y
[tex]x + 25 = y^{2} [/tex]
[tex]y = \sqrt{ (x + 25)} [/tex]
Thus [tex] f^{-1} (x) = \sqrt{(x + 25)} [/tex]
