Define f: n rightarrow z be defined as follows: for each n n, f(n) = 1 + (-1)^n (2n - 1)/4. is the function f an injection? is the function f a surjection? justify your conclusions. suggestions. start by calculating several outputs for the function before you attempt to write a proof. in exploring whether or not the function is an injection, it might be a good idea to uses cases based on whether the inputs are even or odd. in exploring whether f is a surjection, consider using cases based on whether the output is positive or less than or equal to zero.