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

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

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range of f(x)=(x-4)/(5-x)

range

f (x) = \frac{x - 4}{5 - x}

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}{5 - x}

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = \frac{x}{x - 3}

f (x) = - x^{2} - 4 x + 2

f (x) = x + 8

\frac{1}{x + 14}

f (x) = \frac{21 - 7 x}{4 x}

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