What is the range of (5x-3)/(2x+1) ?

The range of (5x-3)/(2x+1) is f(x) 5/2

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range of (5x-3)/(2x+1)

range

\frac{5 x - 3}{2 x + 1}

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{5 x - 3}{2 x + 1}

Inverse of

\frac{5 x - 3}{2 x + 1} : \frac{- 3 - x}{2 x - 5}

\frac{- 3 - x}{2 x - 5}

Find the domain of each inverse function

Domain of

\frac{- 3 - x}{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}

\frac{1}{3} x - 2

\frac{1}{x ^{2} - 2 x - 3}

\frac{1}{x - 5}

f (x) = \frac{4 x + 3}{2 x + 5}

What is the range of (5x-3)/(2x+1) ?
The range of (5x-3)/(2x+1) is f(x)< 5/2 \lor f(x)> 5/2