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

Explanation

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

### Step 1: Prove that \( f(x) \) is one-to-one (injective)

To show that \( f \) is one-to-one, we need to demonstrate that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

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