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

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range of x/(x-6)

range

\frac{x}{x - 6}

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{x - 6}

Inverse of

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

\frac{6 x}{x - 1}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 1 or f (x) > 1

\frac{x ^{2} + 1}{x ^{2} - 1}

y = - x - 3

\frac{( x - 1 )}{x + 2}

\frac{2 x - 1}{x - 7}

f (x) = \frac{1}{x ^{2} - 7 x}