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Is the function #(2-x)^(1/3)# even, odd or neither?

Answer 1

Lily Anderson

It is neither.

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

If it was odd it should be #f(-x)=-f(x)# hence

#f(-x)=(2-(-x))^(1/3)=(2+x)^(1/3)# so it isnt odd

If it was even then #f(-x)=f(x)# hence

#f(-x)=(2-(-x))^(1/3)=(2+x)^(1/3)# so it isnt even as well.

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Answer 2

Cora Alexander

The function ( f(x) = (2-x)^{\frac{1}{3}} ) is neither even nor odd.

For a function to be even, it must satisfy ( f(-x) = f(x) ) for all ( x ) in its domain. For a function to be odd, it must satisfy ( f(-x) = -f(x) ) for all ( x ) in its domain.

However, ( f(x) = (2-x)^{\frac{1}{3}} ) does not satisfy either of these conditions. Therefore, it is neither even nor odd.

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Answer from HIX Tutor

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