What is the range of 2/(x-3) ?

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range of 2/(x-3)

range

\frac{2}{x - 3}

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2}{x - 3}

Inverse of

\frac{2}{x - 3} : \frac{2}{x} + 3

\frac{2}{x} + 3

Find the domain of each inverse function

Domain of

\frac{2}{x} + 3 : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

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

f (x) = \frac{x - 2}{3 x + 5}

f (x) = \frac{x ^{3} - 2 x}{6 x ^{3} + 7 x ^{2} - 5 x}

f (x) = \frac{( 7 x + 8 )}{x - 3}