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

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

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range of x/(x^2-1)

range

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

- \infty < f (x) < \infty

Solution steps

Rewrite as

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

Multiply both sides by

x^{2} - 1

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

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

Discriminant

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

1 + 4 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = \frac{( 3 x + 4 )}{- 5 x - 7}

5 x = 2 y + 10

f (x) = 7 x^{2} - 8 x

f (x) = x^{4} - 8 x^{2} + 1

y = - \frac{1}{2} x - 4

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