What is the range of x/(x-4) ?

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range of x/(x-4)

range

\frac{x}{x - 4}

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 - 4}

Inverse of

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

\frac{4 x}{x - 1}

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

x^{2} - 8 x + 15

f (x) = \frac{- 2 x}{x ^{2} - 16}

y = \frac{6}{7} x - 10

(- 8, 28), (- 4, 16)

(6.6) (2.2)