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

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.

Henceforth...

(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