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y=(x^2-2x+1)/(x^2-2x+2), image of y

Source: Bulgaria 1962 P1

June 24, 2021

algebra

Problem Statement

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

.

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