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

The range of f(x)= 2/(2x-5) is f(x) 0

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

range

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

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2}{2 x - 5}

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{2 + 5 x}{2 x} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

(- 2, - 2), (4, 8)

\frac{x ^{2} - 9}{x ^{2} + 3 x}

3 x^{2} + 5 x - 4

(x - 3)^{2} + 24

What is the range of f(x)= 2/(2x-5) ?
The range of f(x)= 2/(2x-5) is f(x)<0\lor f(x)>0