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How do you know if #h(x) = x / (x^2 - 1)# is an even or odd function?

Answer 1

Serenity Jones

Examine #h(-x)# to see that #h(x)# is an odd function.

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

Then, to see if #h(x)# is even or odd, we examine #h(-x)#.

#h(-x) = (-x)/((-x)^2-1)#

#= -x/(x^2-1)#

#= -h(x)#

Thus #h(x)# is odd.

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Answer 2

Madelyn Anderson

The function ( h(x) = \frac{x}{x^2 - 1} ) 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.

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