Let A = {x ∈ R : −1 ≤ x ≤ 1}. The function f: A → A defined by f(x) = x|x| is:

Let A = {x ∈ R : −1 ≤ x ≤ 1}. The function f: A → A defined by f(x) = x|x| is:

• A. One-one but not onto
• B. Onto but not one-one
• C. Bijective
• D. Neither one-one nor onto

Answer: C) Bijective

Explanation: f(x) = x² for x ≥ 0 and −x² for x < 0. It is strictly increasing on [−1, 1], so it is one-one. Its minimum is f(−1) = −1 and maximum is f(1) = 1. Being continuous, range is [−1, 1] = A, so it's onto.