What is the range of 1/(x-5) ?

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range of 1/(x-5)

range

\frac{1}{x - 5}

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 - 5}

Inverse of

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

\frac{1}{x} + 5

Find the domain of each inverse function

Domain of

\frac{1}{x} + 5 : x < 0 or x > 0

Combine the intervals

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

f (x) = x^{2} e^{4 x}

2 x + 6 y = 1, (- 2, 2)

5 x - 2

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

\frac{7}{x + 3}