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

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

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

range

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

f (x) < \frac{3}{2} or f (x) > \frac{3}{2}

Interval Notation

(- \infty, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{5 + 3 x}{2 x - 3} : x < \frac{3}{2} or x > \frac{3}{2}

Combine the intervals

f (x) < \frac{3}{2} or f (x) > \frac{3}{2}

\frac{25 - x ^{2}}{x + 1}

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

5 x - y = 2

\frac{8 x}{x ^{2} + 1}

f (x) = 4 x^{2} + 9

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