What is the range of (3x)/(x^2-1) ?

The range of (3x)/(x^2-1) is -infinity <f(x)<infinity

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range of (3x)/(x^2-1)

range

\frac{3 x}{x ^{2} - 1}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{3 x}{x ^{2} - 1} = y

Multiply both sides by

x^{2} - 1

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

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

Discriminant

3 x = y (x^{2} - 1) : 9 + 4 y^{2}

9 + 4 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

What is the range of (3x)/(x^2-1) ?
The range of (3x)/(x^2-1) is -infinity <f(x)<infinity