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Is the function #f(x)=(1/x^3+x)^5# even, odd or neither?

Answer 1

Cora Alexander

#f(x) = (1/x^3 + x)^5# is odd.

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

To check this function then, we will look at #f(-x)#.

#f(-x) = (1/(-x)^3 + (-x))^5 = (-1/x^3 -x)^5#

#=> f(-x) = ((-1)(1/x^3 + x))^5 = (-1)^5(1/x^3+x)^5#

#=> f(-x) = -(1/x^3 + x)^5 = -f(x)#

Thus in this case #f(x)# is odd.

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Answer 2

Benjamin Achtenberg

The function ( f(x) = \left(\frac{1}{x^3} + x\right)^5 ) is an odd function.

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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.