What is the range of f(x)=(x-2)/(x+3) ?

The range of f(x)=(x-2)/(x+3) is f(x) 1

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range of f(x)=(x-2)/(x+3)

range

f (x) = \frac{x - 2}{x + 3}

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{x - 2}{x + 3} : \frac{- 2 - 3 x}{x - 1}

\frac{- 2 - 3 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{- 2 - 3 x}{x - 1} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

f (x) = \frac{x - 1}{x ^{2} - 2 x - 3}

f (x) = \frac{x ^{2} + 3 x - 4}{3 x + 3}

f (x) = \frac{1}{x ^{2}} + \frac{1}{2 x - 1}

f (x) = \frac{2 y}{9 + y ^{2}}

What is the range of f(x)=(x-2)/(x+3) ?
The range of f(x)=(x-2)/(x+3) is f(x)<1\lor f(x)>1