How do you determine if #g(x)=3x^5+2x# is an even or odd function?

1 Answer
George C.
May 29, 2016

#g(x)# is an odd function.

Explanation:

The quick way to determine whether a polynomial function is odd or even is to check whether all of its terms are of odd or even degree.

In our example, both #3x^5# and #2x# are of odd degree, so the function is odd.

In general:

  • An even function is a function satisfying #f(-x) = f(x)# for all #x# in its domain.
  • An odd function is a function satisfying #f(-x) = -f(x)# for all #x# in its domain.

In our example:

#g(-x) = 3(-x)^5+2(-x) = -3x^5-2x = -(3x^5+2x) = -g(x)#

So #g(x)# is an odd function.

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