What is the range of (-5x+1)/(5+6x) ?

The range of (-5x+1)/(5+6x) is f(x) -5/6

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range of (-5x+1)/(5+6x)

range

\frac{- 5 x + 1}{5 + 6 x}

f (x) < - \frac{5}{6} or f (x) > - \frac{5}{6}

Interval Notation

(- \infty, - \frac{5}{6}) \cup (- \frac{5}{6}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 5 x + 1}{5 + 6 x}

Inverse of

\frac{- 5 x + 1}{5 + 6 x} : \frac{1 - 5 x}{6 x + 5}

\frac{1 - 5 x}{6 x + 5}

Find the domain of each inverse function

Domain of

\frac{1 - 5 x}{6 x + 5} : x < - \frac{5}{6} or x > - \frac{5}{6}

Combine the intervals

f (x) < - \frac{5}{6} or f (x) > - \frac{5}{6}

f (x) = 1 - x

x - 2 + 5

f (x) = e^{x} - x

(9, 15), (- 1, - 7)

f (x) = \frac{5 x + 4}{7}

What is the range of (-5x+1)/(5+6x) ?
The range of (-5x+1)/(5+6x) is f(x)<-5/6 \lor f(x)>-5/6