Is the function #f(x)=1/(x^3+1)# even, odd or neither?
It is neither .
Hope it helps!!
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To determine if the function (f(x) = \frac{1}{x^3 + 1}) is even, odd, or neither, we need to check its symmetry properties.

Even function: A function (f(x)) is even if (f(x) = f(x)) for all (x) in the function's domain.

Odd function: A function (f(x)) is odd if (f(x) = f(x)) for all (x) in the function's domain.
Let's check the given function:
[f(x) = \frac{1}{x^3 + 1}]
Now, let's evaluate (f(x)):
[f(x) = \frac{1}{(x)^3 + 1} = \frac{1}{x^3 + 1}]
For this function to be even, we need (f(x) = f(x)):
[\frac{1}{x^3 + 1} = \frac{1}{x^3 + 1}]
However, this doesn't hold true, as the denominator changes signs when (x) changes sign, resulting in different function values.
Now, let's check if it's odd:
For the function to be odd, we need (f(x) = f(x)):
[\frac{1}{x^3 + 1} = \frac{1}{x^3 + 1}]
But this also doesn't hold true, as the function values are not negatives of each other.
Thus, the function (f(x) = \frac{1}{x^3 + 1}) is neither even nor odd.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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