Let f : R → R be defined by f(x) = x³ − x. Then f is:

Let f : R → R be defined by f(x) = x³ − x. Then f is:

• A. one-one and onto
• B. onto but not one-one
• C. one-one but not onto
• D. neither one-one nor onto

Answer: B) onto but not one-one

Explanation: f(0) = 0, f(1) = 0, f(−1) = 0 → not one-one. As x → ∞, f(x) → ∞; as x → −∞, f(x) → −∞. Being a continuous polynomial of odd degree, it is onto R.