What is the domain of the function #f(x) = sqrt{x^3 - 3x^2}#?

Answer 1

We are able to rewrite the root and remove squares.

#=sqrt(x^2*(x-3))=xsqrt(x-3)#
Now the #(x-3)# under the root must be non-negative, so the domain is restricted to #x>=3# where #f(x)>=0# graph{sqrt(x^3-3x^2) [-7.26, 24.77, -4.21, 11.82]}
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Answer 2

The domain of the function f(x) = sqrt{x^3 - 3x^2} is all real numbers x such that x^3 - 3x^2 is non-negative, since the square root of a negative number is not defined in the real number system. Therefore, the domain of f(x) is the set of all real numbers x such that x^3 - 3x^2 ≥ 0.

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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.

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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