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

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

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

range

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

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 - 1}{2 x + 5}

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{- 1 - 5 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) = 7 x + 1

x^{5}

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

\frac{x ^{2} + 5}{x ^{2} - 3 x - 10}

\frac{x ^{2} + 10 x + 12}{x ^{2} + 3 x + 2}

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