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

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

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

range

f (x) = \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}

x^{\frac{15}{7}} + x^{\frac{8}{7}}

f (x) = ln (\frac{x + 3}{2 - x})

1 + t^{2}

f (x) = 3 sin (π x)

y = 2 t + tan (t)

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