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

The function f : ℝ → [0, ∞) given by f(x) = x² is:

Answer: Onto but not one-one.

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

Correct answer: D. Onto but not one-one

Explanation: Restricting the codomain to [0, ∞) makes every value attainable, but f(2) = f(−2) still breaks injectivity.

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 →