What is the range of (3x-8)/(7-x) ?

The range of (3x-8)/(7-x) is f(x) -3

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range of (3x-8)/(7-x)

range

\frac{3 x - 8}{7 - x}

f (x) < - 3 or f (x) > - 3

Interval Notation

(- \infty, - 3) \cup (- 3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3 x - 8}{7 - x}

Inverse of

\frac{3 x - 8}{7 - x} : - \frac{- 8 - 7 x}{3 + x}

- \frac{- 8 - 7 x}{3 + x}

Find the domain of each inverse function

Domain of

- \frac{- 8 - 7 x}{3 + x} : x < - 3 or x > - 3

Combine the intervals

f (x) < - 3 or f (x) > - 3

f (x) = \frac{x ( x + 1 ) ( x - 6 )}{x + 8}

f (x) = \frac{x}{2 x - 5}

\frac{5 x - 4}{( x - 7 ) ^{2}}

f (x) = \frac{6 x ^{2} + 7}{8 x + 6}

y = \frac{x ^{2} + 6 x - 7}{x ^{2} + 25}

What is the range of (3x-8)/(7-x) ?
The range of (3x-8)/(7-x) is f(x)<-3\lor f(x)>-3