Let f : [0, ∞) → [0, ∞) be defined by f(x) = x². Then f 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 [0, ∞), f(x₁) = f(x₂) → x₁² = x₂² → x₁ = x₂ (since non-negative) → one-one. Range of f is [0, ∞) → onto. Hence bijective.

imo class 12 relations and functions

Let f : [0, ∞) → [0, ∞) be defined by f(x) = x². Then f is:

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Let f : [0, ∞) → [0, ∞) be defined by f(x) = x². Then f is:

Answer: C) bijective

Explanation: On [0, ∞), f(x₁) = f(x₂) → x₁² = x₂² → x₁ = x₂ (since non-negative) → one-one. Range of f is [0, ∞) → onto. Hence bijective.