What is the range of (x-1)/(x+3) ?

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

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range of (x-1)/(x+3)

range

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = \frac{1}{3} x - 4

f (x) = e^{x - 4}

f (x) = 3 x^{2} - 4 x - 1

2 x + 4 x = 12

(- 3.4) (10)

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