Question

b. Determine whether each of these functions is a bijection from Z to Z.

f (n) = n2 + 1

Answer 1

Let us determine whether the function $f:\mathbb Z\to\mathbb Z,$ $f (n) = n^2 + 1$ is a bijection. Since for $-1\ne 1$ we have that $f(-1)=2=f(1)$, we conclude that the function $f$ is not an injection. Consequently, the function $f$ is not a bijection.