What is the range of f(x)= x/(2x-5) ?

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

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range of f(x)= x/(2x-5)

range

f (x) = \frac{x}{2 x - 5}

f (x) < \frac{1}{2} or f (x) > \frac{1}{2}

Interval Notation

(- \infty, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{2 x - 5}

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{5 x}{2 x - 1} : x < \frac{1}{2} or x > \frac{1}{2}

Combine the intervals

f (x) < \frac{1}{2} or f (x) > \frac{1}{2}

h (x) = \frac{2 x}{x - 11}

2 x + 3 y = 1470

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

f (x) = 5 + 2 x

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