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AP EAMCET202018 Sep 2020Evening ShiftMathematicsFunctionsActual

Exactly how many functions (f: Q Q ) exist such that (f(x+y)=f(x)+f(y) ) and (f(x y) ) (=f(x) f(y) ) for all (x, y Q ) ?

Options

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

Correct answer

B. Two

Step-by-step solution

These functions are simultaneously satisfy for (f(x)=x ) and (f(x)=0 x Q ) Hecne, option (b) is correct.

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