if f(x+y)=f(xy),ybelongs to R,then prove that f is a constant function?

Let x be any real, and y=0.
Then f(x+0) = f(x*0)

=> f(x) = f(0) for all real x.
Hence the function is a constant function. 

Let x be any real, and y=0.
Then f(x+0) = f(x*0)

=> f(x) = f(0) for all real x.
Hence the function is a constant function. BECAUSE IT IS A PROPERTY OF CONSTANT FUNCTION.