sooolve

If f(x+y)=f(x)+f(y) where x,yÎµ R and âˆ«(0 to 1) f(x).dx=1
find f(1)

2 Answers

I assume that f is continuous. In that case, the general solution is f(x)=kx

Hence,
1=\int_0^1 kx\ \mathrm dx = \dfrac{k}{2}
Hence k = 2.
As such f(1)=2.

Thanx...sir .
u mmade this question look soo easy....

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