What is the range of f(x)= x/(x^2-4) ?

The range of f(x)= x/(x^2-4) is -infinity <f(x)<infinity

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range of f(x)= x/(x^2-4)

range

f (x) = \frac{x}{x ^{2} - 4}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x^{2} - 4

x = y (x^{2} - 4)

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

Discriminant

x = y (x^{2} - 4) : 1 + 16 y^{2}

1 + 16 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

What is the range of f(x)= x/(x^2-4) ?
The range of f(x)= x/(x^2-4) is -infinity <f(x)<infinity