What is the range of (9x)/(3-x) ?

The range of (9x)/(3-x) is f(x) -9

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range of (9x)/(3-x)

range

\frac{9 x}{3 - x}

f (x) < - 9 or f (x) > - 9

Interval Notation

(- \infty, - 9) \cup (- 9, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{9 x}{3 - x}

Inverse of

\frac{9 x}{3 - x} : \frac{3 x}{x + 9}

\frac{3 x}{x + 9}

Find the domain of each inverse function

Domain of

\frac{3 x}{x + 9} : x < - 9 or x > - 9

Combine the intervals

f (x) < - 9 or f (x) > - 9

What is the range of (9x)/(3-x) ?
The range of (9x)/(3-x) is f(x)<-9\lor f(x)>-9