# How do you determine if #h(x)= (2x)/(x^3 - x)# is an even or odd function?

Simplify and analyse

Thus, we discover:

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To determine if the function ( h(x) = \frac{2x}{x^3 - x} ) is even or odd, we can use the properties of even and odd functions.

- Even functions satisfy the property ( f(-x) = f(x) ) for all ( x ) in the function's domain.
- Odd functions satisfy the property ( f(-x) = -f(x) ) for all ( x ) in the function's domain.

For the function ( h(x) = \frac{2x}{x^3 - x} ):

- Substitute ( -x ) for ( x ) in the function: ( h(-x) = \frac{2(-x)}{(-x)^3 - (-x)} )
- Simplify the expression: ( h(-x) = \frac{-2x}{-x^3 + x} )
- Compare ( h(-x) ) with ( h(x) ) to determine if it satisfies the properties of even or odd functions.

Since ( h(-x) = \frac{-2x}{-x^3 + x} ) and ( h(x) = \frac{2x}{x^3 - x} ), we can see that ( h(-x) ) is equal to ( -h(x) ), which means the function satisfies the property of an odd function.

Therefore, ( h(x) = \frac{2x}{x^3 - x} ) is an odd function.

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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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