What is the range of f(x)= x/(9x-4) ?

The range of f(x)= x/(9x-4) is f(x) 1/9

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range of f(x)= x/(9x-4)

range

f (x) = \frac{x}{9 x - 4}

f (x) < \frac{1}{9} or f (x) > \frac{1}{9}

Interval Notation

(- \infty, \frac{1}{9}) \cup (\frac{1}{9}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{9 x - 4}

Inverse of

\frac{x}{9 x - 4} : \frac{4 x}{9 x - 1}

\frac{4 x}{9 x - 1}

Find the domain of each inverse function

Domain of

\frac{4 x}{9 x - 1} : x < \frac{1}{9} or x > \frac{1}{9}

Combine the intervals

f (x) < \frac{1}{9} or f (x) > \frac{1}{9}

What is the range of f(x)= x/(9x-4) ?
The range of f(x)= x/(9x-4) is f(x)< 1/9 \lor f(x)> 1/9