Question

Let f(x) = x2 − 81. Find f−1(x).

Answer 1

f(x) = x² - 81

Finding f⁻¹(x) the inverse function

Let y = f(x) and solve for x.

y = x² - 81

y + 81 = x²

x² = y + 81

x = √(y + 81)

Recall f(x) = y, that means x = f⁻¹(y)

x = √(y + 81)

f⁻¹(y) = √(y + 81)

Therefore f⁻¹(x) = √(x + 81)