What is the range of (-4-5x)/(3x-1) ?

The range of (-4-5x)/(3x-1) is f(x) -5/3

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range of (-4-5x)/(3x-1)

range

\frac{- 4 - 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{- 4 - 5 x}{3 x - 1}

Inverse of

\frac{- 4 - 5 x}{3 x - 1} : \frac{- 4 + x}{3 x + 5}

\frac{- 4 + x}{3 x + 5}

Find the domain of each inverse function

Domain of

\frac{- 4 + 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}{2} x^{2}

f (x) = 2 x - 1 + 3

f (x) = a x^{2}

f (x) = \frac{5 x}{x ^{2} - 16}

5 cos (6 x + \frac{π}{2})

What is the range of (-4-5x)/(3x-1) ?
The range of (-4-5x)/(3x-1) is f(x)<-5/3 \lor f(x)>-5/3