It is given that g : {5, 6, 7, 8} → {1, 2, 3, 4} with

g = {(5, 4), (6, 3), (7, 4), (8, 2)}

From the given definition of,

We can see that f is a many one function as:

g(5) = g(7) = 4

= > g is not one- one.

Therefore, function g does not have an inverse.