Let f(x) = √(x^2 + 6x). (We restrict the domain of f to be (−∞, −6) so that we can talk about its inverse.) Without finding a formula for f^−1(x), find (f^−1)’(4).
By definition an inverse function reverses the coordinates of the original function.
If f(x)=y then f^-1(y)=x. In this case that means:
However we were told that the domain is limited to (-oo, -6) so -8 is the only solution for x in this problem.