Question

Which function below is the inverse of f(x) = x2 − 25?

Answer 1

         f(x) = x² - 25
            y = x² - 25
            x = y² - 25
       + 25       + 25
    x + 25 = y²
  √x + 25 = √y²
±√x + 25 = y
±√x + 25 = f⁻¹(x)

Answer 2

$f(x) = x^{2} - 25$
Let f(x)  =  y
  thus y = $x^{2} - 25$
switch the position of y and x in the equation
     $x = y ^{2} - 25$
then solve for y in this case
     $x + 25 = y^{2}$
∴   y=$\sqrt{x + 25}$

Thus, $f^{-1} (x) = \sqrt{x + 25}$