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determine the domain of f when f(x)= 4x[sqr(3-x)]

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Hi Hannah;
f(x)= 4x[sqr(3-x)]
The domain is all the coordinates of the x-axis.
As you already know, you cannot establish the square root of anything less than 0.
(3-x) is greater than 0
-x is greater than (0-3)
-x is greater than -3
x ≤ 3
The domain is...
x is from negative infinity to positive 3.
domain=-∞ to 3