# What is the domain and range of #y= sqrt(x^3)#?

Domain and range:

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Domain: ( x \geq 0 )

Range: ( y \geq 0 )

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The domain of the function ( y = \sqrt{x^3} ) is all real numbers ( x ) such that ( x^3 ) is non-negative, because the square root of a negative number is not defined in the real number system. Since the square root function only accepts non-negative inputs, the domain is restricted to ( x \geq 0 ).

The range of the function ( y = \sqrt{x^3} ) is all real numbers ( y ) such that ( y ) is non-negative, because the square root of a non-negative number is always non-negative. Therefore, the range is ( y \geq 0 ).

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The domain of ( y = \sqrt{x^3} ) is all real numbers ( x ) such that ( x^3 \geq 0 ), which means ( x ) can be any real number.

The range of ( y = \sqrt{x^3} ) is all real numbers ( y ) such that ( y \geq 0 ), since the square root of any real number is non-negative.

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