what is the F-^1
Your notation is confusing and your equation is ambiguous without parentheses.
If F(x) = 6/(x+4) = y,
the inverse function F^-1 (x) is the operation that, if applied to y, will give you x.
x +4 = 6/y
x = (6/y) -4
Finally, switch variables.
F^-1(x) = (6/x) - 4
Note that if you apply this inverse function to 6/(x+4), you get back x.