Is f(x) = x³ a Bijective Function?

Yes, f(x) = x³ is a bijective function from R to R (both one-one and onto).

One-One (Injective) Test: If f(a) = f(b), then a³ = b³ Taking cube roots: a = b Therefore, different inputs always produce different outputs.

Onto (Surjective) Test: For any real number y, we can find x = ∛y such that f(x) = y Since every real number has a real cube root, the range equals the codomain R.

Graphical Insight: The cubic function passes the horizontal line test (one-one) and covers all y-values (onto), making it bijective.

Key Takeaways:

• One-one: strictly increasing function
• Onto: range = R = codomain
• Bijective = has an inverse function f⁻¹(x) = ∛x