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

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

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

range

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

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}{2 x - 1}

Inverse of

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

\frac{x}{2 x - 3}

Find the domain of each inverse function

Domain of

\frac{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}

f (x) = - 2 x^{2} + 2 x

f (x) = x^{\frac{1}{3}}

f (x) = \frac{1}{x - 1}

f (x) = \frac{ln ( x )}{x}

f (x) = 1 + x

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