What is the range of (-4x-7)/(x+2) ?

The range of (-4x-7)/(x+2) is f(x) -4

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range of (-4x-7)/(x+2)

range

\frac{- 4 x - 7}{x + 2}

f (x) < - 4 or f (x) > - 4

Interval Notation

(- \infty, - 4) \cup (- 4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 4 x - 7}{x + 2}

Inverse of

\frac{- 4 x - 7}{x + 2} : \frac{- 7 - 2 x}{x + 4}

\frac{- 7 - 2 x}{x + 4}

Find the domain of each inverse function

Domain of

\frac{- 7 - 2 x}{x + 4} : x < - 4 or x > - 4

Combine the intervals

f (x) < - 4 or f (x) > - 4

What is the range of (-4x-7)/(x+2) ?
The range of (-4x-7)/(x+2) is f(x)<-4\lor f(x)>-4