Grade 11Differential Calculus

**Whether f(x) is a periodic function, where f(x-1)+f(x+1)=sqrt(3)*f(x). If so, what is its period?**

P R Biswas

12 Years agoGrade 11

1 Answer

Sher Mohammad

12 Years ago

$f(x-1)+f(x+1)=\sqrt{3}f(x)$

$f(x)=1/(\sqrt{3})(f(x-1)+f(x+1))$

$f(x+t)=1/(\sqrt{3})(f(x+t-1)+f(x+t+1))$

$1/(\sqrt{3})(f(x+t-1)+f(x+t+1))=1/(\sqrt{3})(f(x-1)+f(x+1))$

$f(x+t-1)+f(x+t+1)=f(x-1)+f(x+1)$

and hence the function is periodic with same period.

Sher Mohammad

B.tech IIT Delhi

Askiitian Faculty

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Whether f(x) is a periodic function, where f(x-1)+f(x+1)=sqrt(3)*f(x). If so, what is its period?

P R Biswas

1 Answer

Sher Mohammad

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