How do you determine if #f(x) = 1/[(3x^3) - 4]# is an even or odd function?

1 Answer
George C.
Jul 13, 2016

#f(x)# is neither even nor odd

Explanation:

An even function is one for which #f(-x) = f(x)# for all #x# in its domain.

An odd function is one for which #f(-x) = -f(x)# for all #x# in its domain.

In our example, we find:

#f(1) = 1/(3-4) = 1/(-1) = -1#

#f(-1) = 1/(-3-4) = 1/(-7) = -1/7#

So neither #f(-1) = f(1)# nor #f(-1) = -f(1)#.

So #f(x)# is neither even nor odd.

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