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

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

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range of f(x)=((x+3))/((x+1))

range

f (x) = \frac{( x + 3 )}{( x + 1 )}

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 + 1}

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

x + 9 + x + 8

(- 3, 2), (2, - 6)

\frac{2 x ^{2} + 4 x - 6}{x ^{2} + 3 x - 10}

f (x) = x - 2 y = 4

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

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