IF f ' (x) =  - f (x)  ,g ( x ) = f ( x ) , F( x ) =  {   [f (x/2)]² + [g (x/2)]²   }and given that F (5)=5 then find F (10)

(a) 5           (b) 10             (c) 0                        (d) 15

pleeeeeeeez tell me how???????/

the basic idea is to F '(x)= 0 . but i m not getting it pleeeeeeeeeeeeeeez help URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I think question should be like this that f"(x)=-f(x) and g'(x)=f(x),otherwise it cannot be proved.

differentiating f(x)

f '(x)=f ' (x) + g '(x) -----(1)

given f '(x)=-f(x) hence f '(x/2)= -f(x/2)

and g(x)= f(x)..........g(x/2)=f(x/2)

substituting in (1)

f '(x)= -f(x/2) + f(x/2)

f ' (x)=0

ie f(x) = constant function

as f(5)=5 given

so f(any value) =5 

so f(10)=5  (ANS)

kya samajh nahin aaya,your question is incorrect i think,i have corrected it and see it now.