Let f be the subset of `Z xxZ`defined by `f = {(a b , a + b) : a , b in Z}`. Is f a function from Z to Z? Justify your answer.

Explanation

To determine whether the subset \( f = \{(ab, a + b) : a, b \in \mathbb{Z}\} \) is a function from \( \mathbb{Z} \) to \( \mathbb{Z} \), we need to verify if every element in the domain (the first component \( ab \)) corresponds to exactly one element in the range (the second component \( a + b \)).

### Step-by-Step Solution:

1. **Understanding the Definition of a Function**:
A relation \( f \) is a function if for every element \( x \) in the domain, there exists a unique element \( y \) in the codomain such that \( f(x) = y \).

2. **Identifying the Domain and Range**:
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