Classify `f: Z->Z` , defined by `f(x)=x^2+x` as injection, surjection or bijection.

Explanation

To classify the function \( f: \mathbb{Z} \to \mathbb{Z} \) defined by \( f(x) = x^2 + x \), we will analyze whether it is injective (one-to-one), surjective (onto), or bijective (both).

### Step 1: Check for Injectivity
A function is injective if different inputs produce different outputs. In mathematical terms, \( f(a) = f(b) \) implies \( a = b \).

1. Assume \( f(a) = f(b) \):
\[
a^2 + a = b^2 + b
...