What is the range of (6x)/(x-2) ?

The range of (6x)/(x-2) is f(x) 6

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range of (6x)/(x-2)

range

\frac{6 x}{x - 2}

f (x) < 6 or f (x) > 6

Interval Notation

(- \infty, 6) \cup (6, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{6 x}{x - 2}

Inverse of

\frac{6 x}{x - 2} : \frac{2 x}{x - 6}

\frac{2 x}{x - 6}

Find the domain of each inverse function

Domain of

\frac{2 x}{x - 6} : x < 6 or x > 6

Combine the intervals

f (x) < 6 or f (x) > 6

f (x) = tan (\frac{x}{3})

x + 8

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

y = 3 x + 4

(- 2, - 6), (5, 2)