imo class 12 relations and functions

Let f: R → R be defined as f(x) = 3x. Choose the correct statement.

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Let f: R → R be defined as f(x) = 3x. Choose the correct statement.

  • A. f is one-one and onto
  • B. f is many-one and onto
  • C. f is one-one but not onto
  • D. f is neither one-one nor onto

Answer: A) f is one-one and onto

Explanation: If f(x₁) = f(x₂), then 3x₁ = 3x₂ → x₁ = x₂, making it one-one. For every y in R, there exists x = y/3 in R such that f(x) = y, making it onto.

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