Let f : R → R be given by f(x) = |x| + 1. The function f is: A. one-one and onto B. one-one but not onto C. onto but not one-one D. neither one-one nor onto Answer: D) neither one-one nor onto Explanation: f(1) = 2, f(−1) = 2 → not one-one. Range is [1, ∞), so not onto R. Hence neither.

imo class 12 relations and functions

Let f : R → R be given by f(x) = |x| + 1. The function f is:

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Let f : R → R be given by f(x) = |x| + 1. The function f is:

Answer: D) neither one-one nor onto

Explanation: f(1) = 2, f(−1) = 2 → not one-one. Range is [1, ∞), so not onto R. Hence neither.