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What is the domain of #(2x^2+x-1)/(x^3-9x)#?

Answer 1

Isaiah Anthony

The domain is all the real values except those who nullify #x^3-9x#

So we have #x^3-9x=0=>x(x^2-9)=0=>x=0,x=3,x=-3#

So the domain is #R-{0,-3,3}# where R is the set of real numbers

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Answer 2

Eva Adamson

The domain of the function ( \frac{2x^2+x-1}{x^3-9x} ) is all real numbers except where the denominator equals zero. So, we find where ( x^3 - 9x = 0 ) and exclude those values from the domain. Factoring the denominator gives ( x(x^2 - 9) = x(x+3)(x-3) ). Therefore, the domain is all real numbers except ( x = 0 ), ( x = 3 ), and ( x = -3 ). So, the domain is ( {x \in \mathbb{R} , | , x \neq 0, \pm 3} ).

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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.