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

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

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

range

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

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 - 3}{x + 2}

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = - \frac{4}{7} x - \frac{16}{7}

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

f (x) = \frac{9}{x}

\frac{x ^{2} - 3 x}{2 x ^{2} + 2 x - 12}

f (x) = e^{x - 7}

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