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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.

11 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points

Dear Sanchit Gupta


f {(x+y) / k } = {f  (x) + f(y) } / k

Put x=y=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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Askiitians Experts

11 years ago
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