Which function below is the inverse of f(x) = x² - 36?
x squared over 36.
±6square root of x
1 over quantity x squared minus 36
± square root of the quantity x plus 36

Solution:

Given function is

f(x) = x² - 36

Let y= f(x) = x² - 36

⇒ y + 36 = x²

⇒ x = ±√y + 36

⇒ x = f(y) → y = f^-1(x)

Swap the variables, y = ±√(x + 36)

± square root of the quantity x plus 36

Therefore, the inverse of the given function is ±√(x + 36)

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

Summary:

The inverse of f(x) = x² - 36 is ±√(x + 36)