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AP EAMCET202017 Sep 2020Evening ShiftMathematicsFunctionsActual

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

Options

  1. A1
  2. B2
  3. C3
  4. DInfinitely many

Correct answer

D. Infinitely many

Step-by-step solution

(F: z z ) (f(x+y)=f(x)+f(y) ) As sum of (z ) integers always gives an integer so, there is no restriction and hence infinite such functions are possible.

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