BG-MO 1962 Problem 1

It is given the expression $y=\frac{x^2-2x+1}{x^2-2x+2}$ , where $x$ is a variable. Prove that:

(a) if $x_1$ and $x_2$ are two values of $x$ , the $y_1$ and $y_2$ are the respective values of $y$ only if $x_1<x_2$ , $y_1<y_2$ ; (b) when $x$ is varying $y$ attains all possible values for which $0\le y<1$ .