Given $f:\mathbb Q\to\mathbb Q$ such that $$f (x+f (x)+2y)=2x+2f (y),$$ how can we prove that the function $f (x)+x$ is surjective ?
The author has just mentioned that the function $f (x)+x$ is surjective without providing slightest of any hint. Following is the picture of the problem with solution
A pedantic and easiest possible explanation and proof for the same would be helpful.