How do you determine if #f(x) =root3x# is an even or odd function?

1 Answer
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Apr 3, 2016

Compare #f(-x)# to #f(x)#.

Explanation:

#f(-x) = root(3)(-x)#

#= - root(3)(x)#

#= -f(x)#

Since #f(-x) = -f(x)#, #f(x)# is an odd function .
# #

Here is a graph of #y = f(x)#.
graph{root(3)(x) [-10, 10, -5, 5]}
In addition, if #f(x)# is an odd function, if you rotate the graph of #y=f(x)# about the origin by 180 degrees, you will get back the same graph. The graph has rotational symmetry about the origin.

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