What is the range of f(x)= 1/(x+4) ?

The range of f(x)= 1/(x+4) is f(x) 0

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range of f(x)= 1/(x+4)

range

f (x) = \frac{1}{x + 4}

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x + 4}

Inverse of

\frac{1}{x + 4} : \frac{1}{x} - 4

\frac{1}{x} - 4

Find the domain of each inverse function

Domain of

\frac{1}{x} - 4 : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

What is the range of f(x)= 1/(x+4) ?
The range of f(x)= 1/(x+4) is f(x)<0\lor f(x)>0