Inequality absolute value If $x>0,y>0$, why does it follow for any $y \in (x,x+1)$, that from:
$$|f(y)-f(x)|<1,$$ we have $$|f(y)| \leq |f(x)|+1$$

$|f(y)| = |(f(y)-f(x))+f(x)| \leq |f(y)-f(x)| + |f(x)| < 1 + |f(x)|$, so. 
