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

The range of x/(6x-5) is f(x) 1/6

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range of x/(6x-5)

range

\frac{x}{6 x - 5}

f (x) < \frac{1}{6} or f (x) > \frac{1}{6}

Interval Notation

(- \infty, \frac{1}{6}) \cup (\frac{1}{6}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{6 x - 5}

Inverse of

\frac{x}{6 x - 5} : \frac{5 x}{6 x - 1}

\frac{5 x}{6 x - 1}

Find the domain of each inverse function

Domain of

\frac{5 x}{6 x - 1} : x < \frac{1}{6} or x > \frac{1}{6}

Combine the intervals

f (x) < \frac{1}{6} or f (x) > \frac{1}{6}

x^{3} + 2 x^{2} + x - 7

f (x) = \frac{1}{5} x - 2

f (x) = 5 x^{2} - 2 x + 2

\frac{1}{x + 3}

- \frac{4}{3} 9

What is the range of x/(6x-5) ?
The range of x/(6x-5) is f(x)< 1/6 \lor f(x)> 1/6