What is the range of f(x)=(3x+6)/(x-1) ?

The range of f(x)=(3x+6)/(x-1) is f(x) 3

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range of f(x)=(3x+6)/(x-1)

range

f (x) = \frac{3 x + 6}{x - 1}

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 - 1}

Inverse of

\frac{3 x + 6}{x - 1} : \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

What is the range of f(x)=(3x+6)/(x-1) ?
The range of f(x)=(3x+6)/(x-1) is f(x)<3\lor f(x)>3