Question

Which function below is the inverse of f(x) = x2 − 36?

Answer 1

\[\large f(x) = x^2 - 36\]
\[\large f^{-1}(x) = ?\]

We replace the 'x' with the 'y' and solve for 'y' again

\[\large y = x^2 - 36\]
\[\large x = y^2 - 36\]
\[\large y^2 = x + 36\]
\[\large y = \sqrt{x + 36}\]

so

\[\large f^{-1}(x) = \sqrt{x + 36}\]