What is the range of (-5x)/(x-8) ?

The range of (-5x)/(x-8) is f(x) -5

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range of (-5x)/(x-8)

range

\frac{- 5 x}{x - 8}

f (x) < - 5 or f (x) > - 5

Interval Notation

(- \infty, - 5) \cup (- 5, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 5 x}{x - 8}

Inverse of

\frac{- 5 x}{x - 8} : \frac{8 x}{x + 5}

\frac{8 x}{x + 5}

Find the domain of each inverse function

Domain of

\frac{8 x}{x + 5} : x < - 5 or x > - 5

Combine the intervals

f (x) < - 5 or f (x) > - 5

\frac{x}{x ^{2} + 5}

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

f (x) = x^{3} + 2 x^{2} + x - 7

5 x^{2} - 5 x

f (x) = 6 x - 5

What is the range of (-5x)/(x-8) ?
The range of (-5x)/(x-8) is f(x)<-5\lor f(x)>-5