Show that `f: R->R` , defined as `f(x)=x^3` , is a bijection.

Explanation

To show that the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^3 \) is a bijection, we need to demonstrate that it is both one-one (injective) and onto (surjective).

### Step 1: Show that \( f(x) = x^3 \) is one-one (injective)

1. **Definition of Injective Function**: A function \( f \) is injective if \( f(a) = f(b) \) implies \( a = b \).

2. **Differentiate \( f(x) \)**: To check if the function is strictly increasing or decreasing, we differentiate \( f(x) \).
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