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NEST2024MathematicsFunctions

For m, n Z , let f_ m, n : Z Z be the function defined as f_ m, n (x)=m x+n for all x Z . Let F be the collection of all such functions, that is, F = f_ m, n : m, n Z . Then

Options

  1. Aevery element of F is bijective
  2. BF has infinitely many elements which are bijective and infinitely many elements which are not bijective
  3. CF has only finitely many elements which are bijective
  4. Dno element of F is bijective

Correct answer

B. F has infinitely many elements which are bijective and infinitely many elements which are not bijective

Step-by-step solution

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