Question

F(x) = -4 - 6. Find the inverse of f(x) and its domain.

Answer 1

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!!!!