Define a function $f\colon\mathbb{R}\to\mathbb{R}$ which is continuous and satisfies
$f(xy)=f(x)f(y)-f(x+y)+1$ for all $x,y\in\mathbb Q$. With a supp condition $f(1)=2$. (I didn't notice that.)
How to show that $f(x)=x+1$ for all $x$ that belong to $\mathbb{R}$?i got the ans from Paul that it is ture for all rationals x but i still cannot show that for $x,y\in\mathbb R$ is correct.