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

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

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

range

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

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}{2 x + 3}

Inverse of

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

y = \frac{- x}{6}

f (x) = \frac{1}{4 x ^{2} - 4 x - 3}

(3, 0), (1, - 10)

(2, 9), (21, 18)

f (x) = \frac{1}{5} x^{2}

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