What is the range of 2/x-3 ?

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range of 2/x-3

range

\frac{2}{x} - 3

f (x) < - 3 or f (x) > - 3

Interval Notation

(- \infty, - 3) \cup (- 3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2}{x} - 3

Inverse of

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

\frac{2}{x + 3}

Find the domain of each inverse function

Domain of

\frac{2}{x + 3} : x < - 3 or x > - 3

Combine the intervals

f (x) < - 3 or f (x) > - 3

f (x) = 3 cos (6 x + \frac{π}{2})

f (x) = - 3

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

f (x) = x^{2} - 7, x \geq 0

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