What is the range of (9x-4)/(5-x) ?

The range of (9x-4)/(5-x) is f(x) -9

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range of (9x-4)/(5-x)

range

\frac{9 x - 4}{5 - x}

f (x) < - 9 or f (x) > - 9

Interval Notation

(- \infty, - 9) \cup (- 9, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{9 x - 4}{5 - x}

Inverse of

\frac{9 x - 4}{5 - x} : - \frac{- 4 - 5 x}{9 + x}

- \frac{- 4 - 5 x}{9 + x}

Find the domain of each inverse function

Domain of

- \frac{- 4 - 5 x}{9 + x} : x < - 9 or x > - 9

Combine the intervals

f (x) < - 9 or f (x) > - 9

2 x - 3 y = 3

f (x) = (x - 2) (x + 1)

f (x) = 20 x - 2 x^{2}

y + 2 x = 5

g (x) = x + 1

What is the range of (9x-4)/(5-x) ?
The range of (9x-4)/(5-x) is f(x)<-9\lor f(x)>-9