Let f(x) =  x2 – 4, x < 0. What is f-1?

To find the inverse of the function f(x) = x² - 4, we first replace f(x) with y:

y = x² - 4

Next, we swap x and y:

x = y² - 4

Then, we solve for y to find the inverse function:

y² = x + 4

y = sqrt(x + 4)

However, since the original function f(x) is defined for x < 0, the inverse function f^-1(x) is defined for x > -4. Also, since the original function only includes negative x-values, we take the negative square root for the inverse function:

f^-1(x) = -sqrt(x + 4), x > -4

So, the inverse function f^-1(x) = -sqrt(x + 4) for x > -4.