How do you determine whether # (2-x)^(1/3)# is an odd or even function?

1 Answer
sente
Jan 3, 2016

#(2-x)^(1/3)# is neither even nor odd.

Explanation:

A function #f(x)# is even if #f(-x) = f(x)#
A function #f(x)# is odd if #f(-x) = -f(x)#

Then, letting #f(x) = (2-x)^(1/3)# we have

#f(-x) = (2-(-x))^(1/3) = (2+x)^(1/3)#

Thus #f(-x) != f(x)# and #f(-x) != -f(x)#

and so #(2-x)^(1/3)# is neither even nor odd.

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