39
Dr.House
·2010-10-12 13:46:40
2)
i dont know if i am being absolutely rubbish
but for f to have period 2a , we must have f(x)=f(x+2a)
putting x=x-a
f(x)=1/2+√[f(x-a)-√f(x-a)]
putting x=x+a
f(x+2a)=1/2+√[f(x+a)-√f(x+a)]
now these 2 are equal only when
f(x-a)=f(x+a)
so f is periodic with period 2a
39
Dr.House
·2010-10-12 13:54:12
1)
f(x)=1/(1-x)
a(0)=x and a(n+1)=f(a(n))
n=0 gives us a(1)=f(x)
so a(2)=f(a(1))=f(f(x))
and a(3)=f(f(f(x)))
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a(n)=f(f(f(.......f(x))))))))))) (n times f occurs)
a(1)=f(x)=1/1-x
a(2)=f(f(x))=f(1/(1-x))=(x-1)/x
a(3)=f(f(f(x)))=f((x-a)/x)=x
a(4) will similarly be 1/(1-x)
and series follows
1/(1-x) , (x-1)/x , x
these keep on occuring one after another
so a(n) willd epend on what remainder n leaves when divided by 3
if its 1 , then a(n)=1/(1-x)
if its 2, then a(n)=(x-1)/x
if its 0, then a(n)=x
39
Dr.House
·2010-10-12 13:55:02
3rd question , please look ta it again , i think u have made some mistake in typing the question