What is the range of f(x)=(2x)/(-4x-20) ?

The range of f(x)=(2x)/(-4x-20) is f(x) -1/2

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range of f(x)=(2x)/(-4x-20)

range

f (x) = \frac{2 x}{- 4 x - 20}

f (x) < - \frac{1}{2} or f (x) > - \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2 x}{- 4 x - 20}

Inverse of

\frac{2 x}{- 4 x - 20} : - \frac{10 x}{2 x + 1}

- \frac{10 x}{2 x + 1}

Find the domain of each inverse function

Domain of

- \frac{10 x}{2 x + 1} : x < - \frac{1}{2} or x > - \frac{1}{2}

Combine the intervals

f (x) < - \frac{1}{2} or f (x) > - \frac{1}{2}

What is the range of f(x)=(2x)/(-4x-20) ?
The range of f(x)=(2x)/(-4x-20) is f(x)<-1/2 \lor f(x)>-1/2