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

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

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

range

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

f (x) < - \frac{4}{3} or f (x) > - \frac{4}{3}

Interval Notation

(- \infty, - \frac{4}{3}) \cup (- \frac{4}{3}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

\frac{3}{3 x + 4}

Find the domain of each inverse function

Domain of

\frac{3}{3 x + 4} : x < - \frac{4}{3} or x > - \frac{4}{3}

Combine the intervals

f (x) < - \frac{4}{3} or f (x) > - \frac{4}{3}

\frac{2}{3 + x}

x^{3} + 6 x^{2}

f (x) = 6 + - x

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

x^{\frac{1}{2}}

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