The easiest way to find an inverse of a function is to substitute the original function's x with y.
y=1/(x-4)-6 ---- original equation
x=1/(y-4)-6 ---- inverted
Now we just need to isolate y again, with a little bit of manipulation this is easy
x+6=1/(y-4)
(x+6)(y-4)=1
y-4=1/(x+6)
y=1/(x+6)+4
We could see that x cannot be -6 since you cannot divide by 0
Therefore the answer to this problem is A
f-1(x)=1/(x+6)+4 where x =/= -6
Hope it helped!!!!
