# How do you find the range of #f(x)= (x^3+1)^-1#?

Determine the domain and range of the inverse function.

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To find the range of the function ( f(x) = (x^3 + 1)^{-1} ), we consider the behavior of the function as ( x ) approaches positive and negative infinity. As ( x ) approaches positive infinity, ( x^3 ) dominates the expression, making ( (x^3 + 1)^{-1} ) approach zero. Similarly, as ( x ) approaches negative infinity, ( x^3 ) dominates the expression, making ( (x^3 + 1)^{-1} ) approach zero. Therefore, the range of the function is all real numbers except zero.

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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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