imo class 12 relations and functions

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

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

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

Answer: C) Bijective

Explanation: On non-negative reals, x₁² = x₂² strictly implies x₁ = x₂, making it one-one. Every non-negative real y has a non-negative real square root √y, making it onto. Thus, it's bijective.

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