Let the signum function f: R → R be defined as f(x) = |x|/x for x ≠ 0, and f(0) = 0. Then f is: A. One-one and onto B. One-one and into C. Many-one and onto D. Many-one and into Answer: D) Many-one and into Explanation: For any x > 0, f(x) = 1, so it is many-one. The range is {−1, 0, 1}, which is a proper subset of R. Thus, it is an into function.

imo class 12 relations and functions

Let the signum function f: R → R be defined as f(x) = |x|/x for x ≠ 0, and f(0) = 0. Then f is:

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Let the signum function f: R → R be defined as f(x) = |x|/x for x ≠ 0, and f(0) = 0. Then f is:

Answer: D) Many-one and into

Explanation: For any x > 0, f(x) = 1, so it is many-one. The range is {−1, 0, 1}, which is a proper subset of R. Thus, it is an into function.