What is the range of f(x)= x/(9x+3) ?

The range of f(x)= x/(9x+3) is f(x) 1/9

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range of f(x)= x/(9x+3)

range

f (x) = \frac{x}{9 x + 3}

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 + 3}

Inverse of

\frac{x}{9 x + 3} : - \frac{3 x}{9 x - 1}

- \frac{3 x}{9 x - 1}

Find the domain of each inverse function

Domain of

- \frac{3 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}

(2, 8), (4, 7)

f (x) = - cos (\frac{1}{2} (x + \frac{π}{2}))

(6, - 6), (- 7, 8)

f (x) = \frac{x ^{2}}{x - 5}

f (x) = 8 x + 12

What is the range of f(x)= x/(9x+3) ?
The range of f(x)= x/(9x+3) is f(x)< 1/9 \lor f(x)> 1/9