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

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

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range of (3x+6)/x

range

\frac{3 x + 6}{x}

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 + 6}{x}

Inverse of

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

\frac{6}{x - 3}

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

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

f (x) = lo g_{2} (x) - 3

f (x) = \frac{- 4 x + 39}{9 x - 52}

f (x) = \frac{x ^{2} - 16}{3 x ^{2}}

f (x) = \frac{9 + x}{6 - x}