What is the range of f(x)=(9x)/(2x-9) ?

The range of f(x)=(9x)/(2x-9) is f(x) 9/2

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range of f(x)=(9x)/(2x-9)

range

f (x) = \frac{9 x}{2 x - 9}

f (x) < \frac{9}{2} or f (x) > \frac{9}{2}

Interval Notation

(- \infty, \frac{9}{2}) \cup (\frac{9}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{9 x}{2 x - 9}

Inverse of

\frac{9 x}{2 x - 9} : \frac{9 x}{2 x - 9}

\frac{9 x}{2 x - 9}

Find the domain of each inverse function

Domain of

\frac{9 x}{2 x - 9} : x < \frac{9}{2} or x > \frac{9}{2}

Combine the intervals

f (x) < \frac{9}{2} or f (x) > \frac{9}{2}

What is the range of f(x)=(9x)/(2x-9) ?
The range of f(x)=(9x)/(2x-9) is f(x)< 9/2 \lor f(x)> 9/2