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

The range of f(x)=-x/(x^2-4) is f(x) 0

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

range

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

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

- \frac{x}{x ^{2} - 4} : \frac{- 1 + 1 + 16 x ^{2}}{2 x}, \frac{- 1 - 1 + 16 x ^{2}}{2 x}

\frac{- 1 + 1 + 16 x ^{2}}{2 x}, \frac{- 1 - 1 + 16 x ^{2}}{2 x}

Find the domain of each inverse function

Domain of

\frac{- 1 + 1 + 16 x ^{2}}{2 x} : x < 0 or x > 0

Domain of

\frac{- 1 - 1 + 16 x ^{2}}{2 x} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

- x^{2} - 4 x + 4

f (x) = \frac{( x ^{2} + 1 )}{3 x - 2 x ^{2}}

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

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

f (x) = - \frac{3}{2} + 1

What is the range of f(x)=-x/(x^2-4) ?
The range of f(x)=-x/(x^2-4) is f(x)<0\lor f(x)>0