7. From the arrow diagram we can see that the function f is not a one-to-one correspondence since it is not one-to-one (both f(1) and f(3) are equal to b) and it is not onto (there is no element x of X for which f(x) = c). Therefore the function f does not have an inverse function.
From the arrow diagram we can see that the function g is a one-to-one correspondence since it is both one-to-one and onto. The arrow diagram for g-1 is: