What is the range of (-2-5x)/(3x-1) ?

The range of (-2-5x)/(3x-1) is f(x) -5/3

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range of (-2-5x)/(3x-1)

range

\frac{- 2 - 5 x}{3 x - 1}

f (x) < - \frac{5}{3} or f (x) > - \frac{5}{3}

Interval Notation

(- \infty, - \frac{5}{3}) \cup (- \frac{5}{3}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 2 - 5 x}{3 x - 1}

Inverse of

\frac{- 2 - 5 x}{3 x - 1} : \frac{- 2 + x}{3 x + 5}

\frac{- 2 + x}{3 x + 5}

Find the domain of each inverse function

Domain of

\frac{- 2 + x}{3 x + 5} : x < - \frac{5}{3} or x > - \frac{5}{3}

Combine the intervals

f (x) < - \frac{5}{3} or f (x) > - \frac{5}{3}

f (x) = - \frac{1}{x ^{2} + 7}

f (x) = \frac{t}{t + 1}

6 (x + 1)^{2} - 5 (x + 1) - 1

f (x) = 15 x^{4} - 15 x^{2}

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

What is the range of (-2-5x)/(3x-1) ?
The range of (-2-5x)/(3x-1) is f(x)<-5/3 \lor f(x)>-5/3