What is the range of 1/x+10 ?

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range of 1/x+10

range

\frac{1}{x} + 10

f (x) < 10 or f (x) > 10

Interval Notation

(- \infty, 10) \cup (10, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x} + 10

Inverse of

\frac{1}{x} + 10 : \frac{1}{x - 10}

\frac{1}{x - 10}

Find the domain of each inverse function

Domain of

\frac{1}{x - 10} : x < 10 or x > 10

Combine the intervals

f (x) < 10 or f (x) > 10

\frac{x ^{2} - 4}{2 x ^{2}}

f (x) = \frac{6}{x + 4} - \frac{1}{2 - x}

f (x) = - ln (x + 1)

(0, - 2), (5, 3)

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