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

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

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

range

\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 x}{x ^{2} + 4}

\frac{7 x}{2 x - 3}

f (x) = - 4 x + 8

f (x) = - 3 sin (2 x + \frac{π}{2})

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

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