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karthik tejaswi Grade: 12
        

how can we find out f(x)?? if something like f(x+y)=f(x)+f(y) is given and it also say f(1)=2 so now also find f(2)..??  for functional equations watz the procedure to find out f(x)??

8 years ago

Answers : (2)

Vanya Saxena
18 Points
										

Hi,


It is given that f(x+y) =f(x)+f(y)  and f(1)=2


      so on keeping x=1 and y=0 in the above eqn we  get


                                  


                                                        f(1)=f(1) +f(0)  =>  f(0)=0  now when we keep x=1 and y=1 we get


  


                                                          f(2)=f(1)+f(1)  =>f(2)=4


 


similarly when we calculate f(3) and f(4) we get them as 6 and 8 respectively.On observing the sequence we come to know that


                                                                      f(x)=2x


 


 

8 years ago
Ramesh V
70 Points
										

put x=y


then f(2x)=2f(x)


so f(0) = 0


given f(1) = 2


so for x=y=1 f(2) = 2f(1) = 4


so f(2) =4


for x= -y


f(x) + f(-x) = 0 


so f(-x) = -f(x)  so f(x) is odd function


if we take f(x) to be a polynomia function then


f(x) is of form (px)2n+1


for p=2 and n=0 , we have f(x) = 2x    which fits in f(0) , f(1) and f(2) .


SO f(x) = 2x


 


 
8 years ago
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