Given information:
Let k:R→R be the function defined by the formula k(x)=(x−1)/x for all real numbers x≠0.
Concept used:
x1 and x2 Are real numbers with x1<x2<0.
Calculation:
Since x1<x2
−x2<−x1 By multiplying by −1 and by the order of the inequality
⇒x1x2−x2<x1x2−x1 By adding x1x2 to both sides
⇒x2(x1−1)<x1(x2−1) By factoring both sides
⇒x1−1x1<x2−1x2 By dividing both sides by the positive numbers x1x2