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

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

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

range

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

f (x) < 2 or f (x) > 2

Interval Notation

(- \infty, 2) \cup (2, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 2 or f (x) > 2

in v erse y = 6^{x}

in v erse f (x) = 2 - x - 5

d i s t an ce (2, 5), (6, 8)

in f l ec t i o n f (x) = 15 x^{4} - 90 x^{2}

in v erse lo g_{0.5} (x)

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