What is the range of f(x)=((x))/((x^{(2))-1)} ?

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

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range of f(x)=((x))/((x^{(2))-1)}

range

f (x) = \frac{( x )}{( x ^{(2)} - 1 )}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \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

\frac{3 x}{8 + x}

tan (\frac{x}{2})

f (x) = x^{2} - 6 x + 10

y - 5 = - 3 x

f (x) = \frac{x - 5}{3 x - 1}

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