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

To find the inverse of the function f(x) = x² – 36, we start by replacing f(x) with y:

y = x² – 36

Now, we need to solve for x in terms of y. We can rearrange the equation:

1. Add 36 to both sides:

y + 36 = x²

2. Next, take the square root of both sides. Remember to consider both the positive and negative roots:

x = ±√(y + 36)

Since functions must pass the vertical line test and have only one output for each input, we typically restrict the domain of the original function to non-negative values (x ≥ 0) when finding the inverse. Thus, we only take the positive root:

So, the inverse function is:

f^-1(y) = √(y + 36)

Thus, the inverse of f(x) = x² – 36 is f^-1(x) = √(x + 36).