Determining the domain of a radical function

The video tutorial explains how to determine the domain of a function involving a radical expression. It covers solving inequalities, emphasizing the importance of flipping the sign when dividing by a negative number. The instructor uses a number line to illustrate the domain, showing that values of X must be less than 2/3. Examples are provided to verify the domain, demonstrating that numbers greater than 2/3 are not included.

What must be true about the expression under the square root in the function f(x) = sqrt(2 - 3x)?

• It must be less than zero.

• It must be equal to zero.

• It must be greater than or equal to zero.

• It can be any real number.

When solving inequalities, what happens to the inequality sign when you divide by a negative number?

• It stays the same.

• It disappears.

• It flips direction.

• It becomes an equality.

Why is the value x = 0 within the domain of the function f(x) = sqrt(2 - 3x)?

• Because 0 results in a negative value under the square root.

• Because 0 results in a positive value under the square root.

• Because 0 is greater than 2/3.

• Because 0 is not a real number.

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

• x = 2/3.

• x < 2/3.

• All real numbers.

• x > 2/3.

What happens when you try to take the square root of a negative number in the context of this function?

• It results in a positive number.

• It results in zero.

• It is undefined.

• It results in a real number.