What is the range of (3x)/(x+6) ?

The range of (3x)/(x+6) is f(x) 3

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range of (3x)/(x+6)

range

\frac{3 x}{x + 6}

f (x) < 3 or f (x) > 3

Interval Notation

(- \infty, 3) \cup (3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3 x}{x + 6}

Inverse of

\frac{3 x}{x + 6} : - \frac{6 x}{x - 3}

- \frac{6 x}{x - 3}

Find the domain of each inverse function

Domain of

- \frac{6 x}{x - 3} : x < 3 or x > 3

Combine the intervals

f (x) < 3 or f (x) > 3

f (x) = - cos (\frac{1}{2} (x - \frac{π}{2})) - 2

f (x) = - 2 sec (\frac{x}{2}) + 3

f (x) = x - 2 + 4

f (x) = (x^{2} - 8 x)^{2} - 8 (x^{2} - 8 x)

f (x) = \frac{x ^{2}}{4 x ^{2} + 7}