What is the range of (2x-1)/(x^2-1) ?

The range of (2x-1)/(x^2-1) is -infinity <f(x)<infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

range of (2x-1)/(x^2-1)

range

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{2 x - 1}{x ^{2} - 1} = y

Multiply both sides by

x^{2} - 1

2 x - 1 = y (x^{2} - 1)

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant

2 x - 1 = y (x^{2} - 1) : 4 + 4 y^{2} - 4 y

4 + 4 y^{2} - 4 y \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

What is the range of (2x-1)/(x^2-1) ?
The range of (2x-1)/(x^2-1) is -infinity <f(x)<infinity