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

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range of x/(x-2)

range

\frac{x}{x - 2}

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 - 2}

Inverse of

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

\frac{2 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{2 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

f (x) = 3 - 4 x + 2

7 x + 2

f (x) = 2 x^{2} + 16 x + 96

f (x) = 0.5 x + 3

f (x) = 1 - cos (x)