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📐 Mathematics  ·  Relations and Functions (Class 12)  ·  JEE

If f : ℝ → ℝ is f(x) = x/(1 + |x|), then f is:

Answer: One-one with range (−1, 1), so not onto ℝ.

  • A One-one with range (−1, 1), so not onto ℝ
  • B Onto ℝ but not one-one
  • C Bijective from ℝ to ℝ
  • D Neither one-one nor onto

Correct answer: A. One-one with range (−1, 1), so not onto ℝ

Explanation: The map is strictly increasing hence injective, but |f(x)| < 1 always, so its range is the open interval (−1, 1).

Concept context

Types of relations, equivalence classes, one-one and onto functions, composition, and invertible functions

Read the full Relations and Functions (Class 12) notes →