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Sanchit Gupta Grade: 12
        

Let f(x) be a deriviable function at x=0 and f {(x+y) / k } = f { (x) + f(y) } / k  for ( k belonging to R and k ≠ 0,2) Then show that f(x) is either zero or odd function.

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Sanchit Gupta


Given


f {(x+y) / k } = {f  (x) + f(y) } / k


Put x=y=0


f(0)=(2/k)f(0)


f(0) [k-2]/k =0


but can not be 2


so f(0) =0


now put y=-x


f(0) =1/k{f(x)+f(-x)}


or   f(-x)=-f(x)


f(x) is a odd function





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Badiuddin

7 years ago
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