Show that the function `f: R->R` given by `f(x)=x^3`is injective.

Explanation

To show that the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^3 \) is injective, we need to prove that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

### Step-by-step Solution:

1. **Assumption**: Assume \( f(x_1) = f(x_2) \) for some \( x_1, x_2 \in \mathbb{R} \).
\[ f(x_1) = f(x_2) \implies x_1^3 = x_2^3 \]
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