What is the range of f(x)=(2x-1)/(4+5x) ?

The range of f(x)=(2x-1)/(4+5x) is f(x) 2/5

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range of f(x)=(2x-1)/(4+5x)

range

f (x) = \frac{2 x - 1}{4 + 5 x}

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2 x - 1}{4 + 5 x}

Inverse of

\frac{2 x - 1}{4 + 5 x} : \frac{- 1 - 4 x}{5 x - 2}

\frac{- 1 - 4 x}{5 x - 2}

Find the domain of each inverse function

Domain of

\frac{- 1 - 4 x}{5 x - 2} : x < \frac{2}{5} or x > \frac{2}{5}

Combine the intervals

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

What is the range of f(x)=(2x-1)/(4+5x) ?
The range of f(x)=(2x-1)/(4+5x) is f(x)< 2/5 \lor f(x)> 2/5