f(x) = (x+2)/(x+6)

Question

What is f^(-1)(-6)? (what is f inverse of -6)

I found f' which was [(x+6)-(x+2)]/(x+6)^2

I set the function equal to -6 and found x to be -30/7.

Used the formula to find inverse function: 1/f'(f^(-1)(-6))

So I replaced f^(-1)(-6) with -30/7 and then the new equation is 1/f'(-30/7)

I got 0.0816327 which is incorrect. Help?

Answer 1

f^-1 of (-6) is the value of x that makes f(x) = -6
(x+2)/(x+6) = -6
x +2 = -6x - 36
7x = -38
x = -5.428

Check: x+2/(x+6) = -3.428/0.572 =-6

Answer 2

I think I did wrong math and ended up doing more than I was supposed to. Thanks for the help, I get it now!