What is the range of x+1/x ?

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range of x+1/x

range

x + \frac{1}{x}

f (x) \leq - 2 or f (x) \geq 2

Interval Notation

(- \infty, - 2] \cup [2, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

x + \frac{1}{x}

Inverse of

x + \frac{1}{x} : \frac{x + x ^{2} - 4}{2}, \frac{x - x ^{2} - 4}{2}

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

Find the domain of each inverse function

Domain of

\frac{x + x ^{2} - 4}{2} : x \leq - 2 or x \geq 2

Domain of

\frac{x - x ^{2} - 4}{2} : x \leq - 2 or x \geq 2

Combine the intervals

f (x) \leq - 2 or f (x) \geq 2

f (x) = 8^{x + 1} - 3

x^{2} - 2 x - 1

f (x) = \frac{x ^{2} - 4}{x + 3}

f (x) = - 11 - x

\frac{2}{x - 1}