What is the range of (4-5x)/(2x) ?

The range of (4-5x)/(2x) is f(x) -5/2

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range of (4-5x)/(2x)

range

f (x) < - \frac{5}{2} or f (x) > - \frac{5}{2}

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- \frac{5}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4 - 5 x}{2 x}

Inverse of

\frac{4 - 5 x}{2 x} : \frac{4}{2 x + 5}

\frac{4}{2 x + 5}

Find the domain of each inverse function

Domain of

\frac{4}{2 x + 5} : x < - \frac{5}{2} or x > - \frac{5}{2}

Combine the intervals

f (x) < - \frac{5}{2} or f (x) > - \frac{5}{2}

What is the range of (4-5x)/(2x) ?
The range of (4-5x)/(2x) is f(x)<-5/2 \lor f(x)>-5/2