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

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range of 2/(2-x)

range

\frac{2}{2 - x}

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}

Inverse of

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

- \frac{2 - 2 x}{x}

Find the domain of each inverse function

Domain of

- \frac{2 - 2 x}{x} : x < 0 or x > 0

Combine the intervals

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

f (x) = 5 x^{4} - 30 x^{2}

\frac{x ^{2} - 4}{x ^{2} - 1}

f (x) = - \frac{x - 1}{x + 3}

(7.7) (13.13)

(- 6, 3), (8, - 3)