BMAD Posted May 26, 2022 Report Share Posted May 26, 2022 2f(1/x)-f(x)+2f(2/x)-f(x/2) = x, x is defined on the reals except where x =0 find f(x) = 1 Quote Link to comment Share on other sites More sharing options...

0 EventHorizon Posted May 26, 2022 Report Share Posted May 26, 2022 Spoiler 2f(1/x)-f(x) = 2x/3 (plugging in x/2 for x then adding to this gives original) f(x) = 2f(1/x) - 2x/3 (rearrange) f(1/x) = 2f(x) - 2/3x (substitute 1/x for x) f(x) = 2(2f(x) - 2/3x) - 2x/3 (replace f(1/x) from two above) f(x) = 4f(x) - 4/3x - 2x/3 3f(x) = 4/3x + 2x/3 f(x) = (2/9)(x+2/x) Quote Link to comment Share on other sites More sharing options...

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## BMAD

2f(1/x)-f(x)+2f(2/x)-f(x/2) = x, x is defined on the reals except where x =0

find f(x) =

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