If f^(-1) is the inverse of f, then
f(f^(-1)(x)) = x
It looks like f(x) = (x + a)/x. This gives us
f(f^(-1)(x)) = (f^(-1)(x) + a)/f^(-1)(x) = x
Solve for f^(-1)(x) :
f^(-1)(x) + a = x f^(-1)(x)
f^(-1)(x) - x f^(-1)(x) = -a
(1 - x) f^(-1)(x) = -a
f^(-1)(x) = -a/(1 - x)
f^(-1)(x) = a/(x - 1)
If a = 4, then the inverse is f^(-1)(x) = 4/(x - 1).
