Show that the function `f: R->R` defined by `f(x)=3x^3+5` for all `x in R` is a bijection.

Explanation

To show that the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 3x^3 + 5 \) is a bijection, we need to prove that it is both one-to-one (injective) and onto (surjective).

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

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

1. Assume \( f(a) = f(b) \).
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