Let `f : R->R`be defined as `f(x) = 3x`. Choose the correct answer. (A) f is one-one onto (B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto.

Explanation

To determine the properties of the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 3x \), we need to check if the function is one-one (injective) and onto (surjective).

### Step 1: Check if the function is one-one (injective)

A function is one-one if for every pair of distinct inputs, the outputs are also distinct. In mathematical terms, we need to show that if \( f(a) = f(b) \), then \( a = b \).

1. Assume \( f(a) = f(b) \).
2. This means \( 3a = 3b \).
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