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How to find the Range of a function #f(x)= (x^3+1)^-1#?

Answer 1

#f(x) = (x^3+1)^(-1)# is equivalent to #f(x) = 1/(x^3+1)# which is valid for all Real values of #x# except when #(x^3+1) = 0#

#(x^3+1) = 0# implies #x=1#

So the Domain of #f(x)# is all Real numbers except #1# or in set notation Domain of #f(x) = {(-oo,1) uu (1,+oo)}#

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Answer 2

Eva Abramson

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

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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.