Classify `f: R->R` , defined by `f(x)=|x|` as injection, surjection or bijection.

Explanation

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

### Step 1: Check for Injectivity (One-to-One)
A function is injective if different inputs map to different outputs. In other words, if \( f(a) = f(b) \), then it must follow that \( a = b \).

- For the function \( f(x) = |x| \):
- Let’s assume \( f(a) = f(b) \).
- This means \( |a| = |b| \).
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