For each of the given we have Z_100= {0,1,2,3,....,99} with a and b as element of Z_100 and f: Z_100--->Z_100 is a function stated by f(x)=ax+b(mod 100). In order words, when you find f(x) you find element in Z_100 which is congruent to ax+b modulo 100.
i) Prove that if a is either even or multiple of 5, then f is not one-to-one.
ii) Prove that if a is neither even nor multiple of 5, then f is one-to-one