What is the range of (6x-8)/(5-x) ?

The range of (6x-8)/(5-x) is f(x) -6

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range of (6x-8)/(5-x)

range

\frac{6 x - 8}{5 - x}

f (x) < - 6 or f (x) > - 6

Interval Notation

(- \infty, - 6) \cup (- 6, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{6 x - 8}{5 - x}

Inverse of

\frac{6 x - 8}{5 - x} : - \frac{- 8 - 5 x}{6 + x}

- \frac{- 8 - 5 x}{6 + x}

Find the domain of each inverse function

Domain of

- \frac{- 8 - 5 x}{6 + x} : x < - 6 or x > - 6

Combine the intervals

f (x) < - 6 or f (x) > - 6

f (x) = \frac{x ^{7} - 7}{9}

f (x) = x + 18

f (x) = \frac{2 x - 1}{x ^{2} - 2 x - 8}

(x - 6)^{2}

f (x) = \frac{1}{( x - 1 )}

What is the range of (6x-8)/(5-x) ?
The range of (6x-8)/(5-x) is f(x)<-6\lor f(x)>-6