What is the range of 1/(x-6) ?

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range of 1/(x-6)

range

\frac{1}{x - 6}

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{1}{x - 6}

Inverse of

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

\frac{1}{x} + 6

Find the domain of each inverse function

Domain of

\frac{1}{x} + 6 : x < 0 or x > 0

Combine the intervals

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

f (x) = 2 x^{3} - 5

f (x) = 2 + 4 sin (3 x + \frac{π}{2})

f (x) = \frac{7}{x ^{2} - 49}

\frac{2}{x ^{2} + 4 x + 3}

\frac{x + 1}{x + 6}