Discuss the surjectivity of `f: Z->Z` given by `f(x)=3x+2` for all `x in Z` .

Explanation

To determine whether the function \( f: \mathbb{Z} \to \mathbb{Z} \) defined by \( f(x) = 3x + 2 \) is surjective, we need to check if every integer \( y \) in the codomain can be expressed as \( f(x) \) for some integer \( x \).

### Step-by-step Solution:

1. **Understanding Surjectivity**: A function is surjective (onto) if for every element \( y \) in the codomain, there exists an element \( x \) in the domain such that \( f(x) = y \).

2. **Setting Up the Equation**: We want to find \( x \) such that:
\[
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