Correct Option: A function is one-one if f(x1) = f(x2) implies x1 = x2. Here, f(1) = |1| = 1 and f(-1) = |-1| = 1. Since 1 ≠ -1 but they have the same image, it is not one-one. A function is onto if the Range equals the Codomain. The Range of |x| is [0, ∞), but the Codomain is given as R. Since negative real numbers in the codomain have no pre-image, it is not onto. Incorrect Options: All other options claim the function is either one-one or onto (or both), which contradicts the basic definition and range of the modulus function.