What is the range of 1/x-4 ?

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range of 1/x-4

range

\frac{1}{x} - 4

f (x) < - 4 or f (x) > - 4

Interval Notation

(- \infty, - 4) \cup (- 4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x} - 4

Inverse of

\frac{1}{x} - 4 : \frac{1}{x + 4}

\frac{1}{x + 4}

Find the domain of each inverse function

Domain of

\frac{1}{x + 4} : x < - 4 or x > - 4

Combine the intervals

f (x) < - 4 or f (x) > - 4

\frac{x ^{2} - x}{x ^{2} - 5 x + 4}

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

f (x) = 4 x - 3

ln (64.86)

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