IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

man111

(1) if f(x)+f(x+f(y))=2x+y

than find out all these function.

Indian_Dragon

one of the functions is f(x)= x

sol.

f(x) + f(x+f(y))=

=x + f(x+y)

=x+ (x+y)

=2x + y.

may be there r more.

konichiwa2x

yep, so far I too was able to find only 1 such function.

Substitue x,y = 0. Gives us:

Closer inspection shows us that

hsbhatt

Suppose that f(x) = 0 for some value x =k

Then 2f(x) = 2x+k

or f(x) = x+k/2

But we have with x=0 and y=k, f(0)+f(k) = k which means k/2 = k and hence k =0

So f(x) = x is the only function in this class

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