What is the range of (5x-2)/(x+9) ?

The range of (5x-2)/(x+9) is f(x) 5

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range of (5x-2)/(x+9)

range

\frac{5 x - 2}{x + 9}

f (x) < 5 or f (x) > 5

Interval Notation

(- \infty, 5) \cup (5, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{5 x - 2}{x + 9}

Inverse of

\frac{5 x - 2}{x + 9} : \frac{- 2 - 9 x}{x - 5}

\frac{- 2 - 9 x}{x - 5}

Find the domain of each inverse function

Domain of

\frac{- 2 - 9 x}{x - 5} : x < 5 or x > 5

Combine the intervals

f (x) < 5 or f (x) > 5

What is the range of (5x-2)/(x+9) ?
The range of (5x-2)/(x+9) is f(x)<5\lor f(x)>5