a) f(n) is the number of students in your calculus class whose birthday is on the nth day of the year.
f(n) is not invertible because several different days, n, may have the same number of students, f(n). Then for one specific f(n) you cannot determine a unique n.
b) f(x) is the volume in litters of x kilograms of water at 4 degrees celsius.?
f(x) is invertible because each x gives a different f(x), then you can determine unambiguously which f(x) corresponds to each x.