The function `f: R->R` , `f(x)=x^2` is (a) injective but not surjective (b) surjective but not injective (c) injective as well as surjective (d) neither injective nor surjective

Explanation

To determine whether the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^2 \) is injective or surjective, we will analyze both properties step by step.

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

A function is injective if different inputs map to different outputs. In mathematical terms, if \( f(x_1) = f(x_2) \), then it must follow that \( x_1 = x_2 \).

1. Assume \( f(x_1) = f(x_2) \).
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