period

if f(x) belogs [1,2] when x belongs R and for a fixd positive real no P. f(x+p)=1+√2f(x)-f(x)^2.

prove that f(x) is periodic.

5 Answers

341

Hari Shankar ·2009-06-11 08:28:25

(f(x+p) -1)² = 1-(f(x)-1)²

Hence f(x) = 1 + \sqrt{2 f(x+p) - f^2(x+p)}

Hence f(x-p) = 1 + \sqrt{2 f(x) - f^2(x)}

Thus we have f(x-p) = f(x+p) so that 2p is a period of f(x)

sir the exp is

f(x+p)=1+\sqrt{2f(x)}-{f(x)}^{2}

msp Q typed wrongly in ur textbook

whats the question here ????

THe question has been discussed a couple of times eureka.. I am sure you must have seen.. Read Prophet sir's thread...

That is the question..

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