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AP EAMCET202017 Sep 2020Morning ShiftMathematicsFunctionsActual

How many bijections (f: Z Z ) are there such that (f(x+y)=f(x)+f(y) ) for all (x, y Z ) ?

Options

  1. AOne
  2. BTwo
  3. CThree
  4. DInfinitely many

Correct answer

D. Infinitely many

Step-by-step solution

(f: Z Z ) ( aligned & f(x+y)=f(x)+f(y) ; x, y Z & f(x)=k x aligned ) So, there are infinitely many bijections

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