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.

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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 &ne; 0,2) Then show that f(x) is either zero or odd function.

Badiuddin askIITians.ismu Expert · Answer

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 Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best Sanchit. Regards, Askiitians Experts Badiuddin

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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.

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.

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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.

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.

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