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

Odd.

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To determine if ( f(x) = \frac{{x^2 - 1}}{{2x}} ) is an even or odd function, we evaluate ( f(-x) ) and compare it to ( f(x) ):

If ( f(-x) = f(x) ), then the function is even. If ( f(-x) = -f(x) ), then the function is odd.

So, let's evaluate ( f(-x) ):

[ f(-x) = \frac{{(-x)^2 - 1}}{{2(-x)}} = \frac{{x^2 - 1}}{{-2x}} = -\frac{{x^2 - 1}}{{2x}} = -f(x) ]

Since ( f(-x) = -f(x) ), the function is odd.

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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.

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.

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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