Give examples of two functions `f: N->Z" and "g: Z->Z`such that gof is injective but g is not injective. (Hint: Consider `f(x) = x" and "g(x) = |x|`)

Explanation

To solve the problem, we need to find two functions \( f: \mathbb{N} \to \mathbb{Z} \) and \( g: \mathbb{Z} \to \mathbb{Z} \) such that the composition \( g \circ f \) is injective, while \( g \) itself is not injective.

### Step 1: Define the function \( f \)
Let us define the function \( f \) as follows:
\[ f(x) = x \]
This function takes a natural number \( x \) and maps it to the same integer \( x \). The domain of \( f \) is \( \mathbb{N} \) (natural numbers), and the range is \( \mathbb{Z} \) (integers).
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