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

Answer 1

odd function

FIRST YOU NEED TO KNOW : 1.EVEN FUNCTION #f(x)=f(-x)# these type of function symmetry to y-axis 2.ODD FUNCTION #f(x)=-f(-x)#these type of function symmetry to #O(0,0)#

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

because

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

thus it's a strange function.

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Answer 2

Elias Ackerman

To determine if a function ( f(x) = 1 - x^{1/3} ) is even or odd, we can examine its symmetry properties:

Even functions satisfy the condition: ( f(-x) = f(x) ).
Odd functions satisfy the condition: ( f(-x) = -f(x) ).

Substituting ( -x ) into the function and simplifying, we have:

[ f(-x) = 1 - (-x)^{1/3} = 1 + x^{1/3} ]

Comparing ( f(-x) ) with ( f(x) ), we observe that ( f(-x) ) is not equal to ( f(x) ) and neither is it equal to the negative of ( f(x) ). Therefore, the function ( f(x) = 1 - x^{1/3} ) does not satisfy the conditions for even or odd functions. In other words, it is neither even nor odd.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.