Question by Lê Quốc Trần Anh - Discuss with MathYouLike

Lê Quốc Trần Anh Coordinator

12/06/2018 at 11:45

Given f(x) satisfys: \(x\cdot f\left(x+2018\right)=\left(x+2016\right)\cdot f\left(x\right)\). Prove that f(x) = 0 with x = 0 and -2018.

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Alone 14/06/2018 at 01:00

With x=0 then \(0.f\left(2018\right)=2016.f\left(0\right)\Rightarrow f\left(0\right)=0\)

With x=-2018 then \(-2018.f\left(-2018+2018\right)=\left(-2018+2016\right).f\left(-2018\right)\)

\(\Rightarrow-2018.f\left(0\right)=-2.f\left(-2018\right)\).Because \(f\left(0\right)=0\) so \(-2f\left(-2018\right)=0\Rightarrow f\left(-2018\right)=0\)

So \(f\left(x\right)=0\) with x=0 and -2018

So
Lê Quốc Trần Anh selected this answer.

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