What is the range of (x+4)/(x-5) ?

The range of (x+4)/(x-5) is f(x) 1

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range of (x+4)/(x-5)

range

\frac{x + 4}{x - 5}

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x + 4}{x - 5}

Inverse of

\frac{x + 4}{x - 5} : \frac{4 + 5 x}{x - 1}

\frac{4 + 5 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{4 + 5 x}{x - 1} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

What is the range of (x+4)/(x-5) ?
The range of (x+4)/(x-5) is f(x)<1\lor f(x)>1