1i have many questions (and few wid answers) which are very interesting saved offline in my desktop... :)
1 .check whether the function defined by
f(x+m)=1+ √[2f(x)-f2(x)]
…..for all x E R is periodic or not.
2. Find all functions f satisfying the identity,
f(x)+ f((x-1)/x)=1+x,
…… for all xER-{0,1}.
3. Find the domain n range of h(x)=g(f(x)),where…
f(x)= [x], -2≤ x ≤-1
= |x|+1, -1<x≤2
and,
g(x)=[x], -pi≤x≤0
= sinx, 0<x≤pi.
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6 Answers
1solution 2....
nishant bhaiya's rep::
Such questions are sort of standard question...
see the trick is to keep substituting x with something such that it becomes the next term...
first subst x=(x-1)/x
you get an equation
u will get f(1/(1-x))+f(1-1/x) = 1/(1-x)-x
then substract the second from the first equation
u will get f(x)-f(1/(1-x)) = x+1/x-1
Now put x=1/(1-x) again using the same trick as above....
u will get f(1/(1-x))-f(1-1/x) = 2-1/x
The 2nd and 4th are simultaneous..
U can go on to get it in a single term.. I hope this helps u get the full solution
hey gr8.. u had his answer saved!
We lost 2 day's data due to some database misadventure :)
1
62hey great.. why dont u post them.. we will do some brain storming on them :)
1arrey nooooooooooo........... i was talking of questions posted on this site........
i have them offline as well.......dats y i cud post a few of them today wen u said all in 2 day's got deleted.......