What is the range of-(5x)/(x-6) ?

The range of-(5x)/(x-6) is f(x) -5

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range of-(5x)/(x-6)

range

- \frac{5 x}{x - 6}

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 - 6}

Inverse of

- \frac{5 x}{x - 6} : \frac{6 x}{x + 5}

\frac{6 x}{x + 5}

Find the domain of each inverse function

Domain of

\frac{6 x}{x + 5} : x < - 5 or x > - 5

Combine the intervals

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

f (x) = e^{2 x}

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

f (x) = 3 \cdot 2^{x}

y = sin (2 x ln (x)) (sin^{2} (2 x))

(1, 1), (8, - \frac{3}{4})

What is the range of-(5x)/(x-6) ?
The range of-(5x)/(x-6) is f(x)<-5\lor f(x)>-5