Verified Answer :

Panoyin

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)

JoshEast

\(f(x) = x^{2} - 25\)
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, \(f^{-1} (x) = \sqrt{x + 25}\)

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