Prove that the function `f : R ->R`, given by `f (x) = 2x`, is one-one and onto.

Explanation

To prove that the function \( f : \mathbb{R} \to \mathbb{R} \) given by \( f(x) = 2x \) is one-one (injective) and onto (surjective), we will follow these steps:

### Step 1: Prove that \( f \) is one-one (injective)

To show that \( f \) is one-one, we need to prove that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

1. Assume \( f(x_1) = f(x_2) \).
2. This means \( 2x_1 = 2x_2 \).
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