How do you determine whether the function is a polynomial function $f(x) = 2 - 2/x^6$ ?

Question

5854 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-27T22:25:08

$"the function:" \quad f(x) \ = \ 2 - 2/x^6, \quad "is not a polynomial function."$

$"Please see argument below."$

$"We are given:" \qquad \qquad \qquad \qquad f(x) \ = \ 2 - 2/x^6.$

$"One way of deciding if this function is a polynomial function is"$
$"the following:"$

$"1) We observe that this function," \ f(x), "is undefined at" \ x=0.$

$"2) However, we recall that polynomial functions are, certainly,"$
$\qquad \qquad "defined everywhere."$

$"So" \ f(x) \ "cannot be a polynomial function."$

$"Hence, we conclude immediately:"$

$"the function:" \quad f(x) \ = \ 2 - 2/x^6, \quad "is not a polynomial function."$

How do you determine whether the function is a polynomial function f(x) = 2 - 2/x^6f(x) = 2 - 2/x^6?