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

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

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

range

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

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x^{2} - 1

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

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

Discriminant

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

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

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = 3 x + 1

(3, - 4), (- 1, 6)

2 + 4 + 11 x

x^{\frac{4}{3}} + 4 x^{\frac{1}{3}}

\frac{4}{2 - x}

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