Show that the function `f: N->N` given by `f(1)=f(2)=1` and `f(x)=x-1` for every `xgeq2` , is onto but not one-one.

Explanation

To show that the function \( f: \mathbb{N} \to \mathbb{N} \) defined by \( f(1) = f(2) = 1 \) and \( f(x) = x - 1 \) for every \( x \geq 2 \) is onto but not one-one, we will proceed step by step.

### Step 1: Show that the function is not one-one

1. **Definition of One-One Function**: A function \( f \) is one-one (injective) if \( f(x_1) = f(x_2) \) implies \( x_1 = x_2 \).

2. **Evaluate the Function**:
- We have \( f(1) = 1 \) and \( f(2) = 1 \).
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