What is the range of 1/(x+4)+3 ?

The range of 1/(x+4)+3 is f(x) 3

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range of 1/(x+4)+3

range

\frac{1}{x + 4} + 3

f (x) < 3 or f (x) > 3

Interval Notation

(- \infty, 3) \cup (3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x + 4} + 3

Inverse of

\frac{1}{x + 4} + 3 : \frac{- 4 x + 13}{x - 3}

\frac{- 4 x + 13}{x - 3}

Find the domain of each inverse function

Domain of

\frac{- 4 x + 13}{x - 3} : x < 3 or x > 3

Combine the intervals

f (x) < 3 or f (x) > 3

y = - 2 x + 5

\frac{490 \cdot e ^{3 x}}{4 + e ^{3 x}}

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

f (x) = - 7 x^{3}

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