This-x-3-x-2-x-4-3x-2-1-find-the-sphere-of-function-values-

Question Number 12591 by @ANTARES_VY last updated on 26/Apr/17

This

\oint (x) = 3 - \frac{x^{2}}{x^{4} + 3 x^{2} + 1} find the

sphere of function values

Commented by ajfour last updated on 26/Apr/17

\oint (x) = 3 - \frac{1}{{(x + \frac{1}{x})}^{2} + 1} (i f x \neq 0)

a t x = 1, \oint (x) h a s l e a s t v a l u e

= 3 - \frac{1}{5}

w h e n x \to \pm \infty, \oint (x) \to 3

a n d i f x = 0, \oint (x) = 3

s o r a n g e o f \oint (x) i s [\frac{14}{5}, 3] .

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