Show that the function `f : R ->R`, defined as `f(x)=x^2`, is neither one-one nor onto.

Explanation

To show that the function \( f : \mathbb{R} \to \mathbb{R} \), defined as \( f(x) = x^2 \), is neither one-one nor onto, we will analyze both properties step by step.

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

A function is one-one (injective) if different inputs produce different outputs. In other words, if \( f(x_1) = f(x_2) \), then it must imply that \( x_1 = x_2 \).

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