Question

f(x)= square root (3x)
whats the rational zero(s)?
whats the domain?

Answer 1

Domain is the thing you are inputting in f, which is x.

Equate f(x) with 0 for the second part.

Answer 2

\( \color{Black}{\Rightarrow 0 = \sqrt{3x}}\)

Answer 3

The zero(s) of a function is the value of x such that f(x) = 0. Thus to find the zero(s) of a function, let f(x) = 0 then solve for x.
f(x) = sqrt (3x) = =
sqrt (3x) = 0. Square both sides, we obtain
3x = 0 or x = 0
Hence 0 is the only zero of the given function.

The domain of a function is the values of x such that the function f(x) is defined. Since we cannot have negative number under the square root so that f(x) is a real number,
3x >= 0 or x >=0
Therefore, the domain of the given function is all real numbers greater or equal to 0.

Answer 4

Typo on the third line. It should have been
f(x) = sqrt (3x) = 0
I apologize :)