What is the range of 1/x+3 ?

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range of 1/x+3

range

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

Inverse of

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

\frac{1}{x - 3}

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

d o main f (x) = ∣ x - 4 ∣

m o n o t o n e x^{4} - \frac{4}{3} x^{3} - 4 x^{2} + 7

in t erce pt s f (x) = 2 x^{2} + 5 x + 3

l in e (0, 0), (h, r)

d o main f (x) = \frac{x}{x + 5}