In: Advanced Math
For the following functions, determine if they are injective, surjective, bijective, or none and explain the reason. Recall that R: is the set of real numbers, Z: the set of Integers, and N: the set of natural numbers.
a. f: R → Z, where f(x) = ceiling(x)
b. f: Z → Z defined by f(x) = √5? + 1
c. f: Z → N defined by f(x) = |x + 1|