How do you determine if #f(x)= 2x^3+6x # is an even or odd function?

1 Answer
Ananda Dasgupta
Jul 31, 2016

You substitute #-x# in place of #x# everywhere. If #f(-x)=-f(x)#, as in the case of the given function, it is odd.

Explanation:

#f(-x) = 2(-x)^3+6(-x)#

#= 2(-x^3)-6x#
#=-2x^3-6x#
# =-(2x^3+6x)#
#=-f(x)#

Note : This particular function can be easily recognized as odd in one glance, as it comprises of only odd powers of #x#

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