Understanding the Domain of a Function

The video tutorial explains how to find the domain of the function f(x) = √(2x - 8). It defines the domain as the set of all possible valid inputs for which the function is defined. The function is only defined when the expression under the square root, 2x - 8, is non-negative. The tutorial solves the inequality 2x - 8 ≥ 0 to determine that x must be greater than or equal to 4. Thus, the domain of the function is all real numbers greater than or equal to 4.

What is the domain of a function?

• The set of all real numbers.

• The range of values the function can take.

• The set of all possible inputs for which the function is defined.

• The set of all possible outputs of the function.

For the function f(x) = √(2x - 8), when is it defined?

• When 2x - 8 is less than 0.

• When 2x - 8 is a negative number.

• When 2x - 8 is equal to 0.

• When 2x - 8 is greater than or equal to 0.

Why must 2x - 8 be non-negative for the function to be defined?

• Because the square root of a negative number is negative.

• Because the square root of a negative number is undefined in real numbers.

• Because the square root of a negative number is a positive number.

• Because the square root of a negative number is zero.

What is the first step in solving the inequality 2x - 8 ≥ 0?

• Divide both sides by 2.

• Subtract 8 from both sides.

• Add 8 to both sides.

• Multiply both sides by 2.

After adding 8 to both sides of the inequality 2x - 8 ≥ 0, what is the next step?

• Multiply both sides by 2.

• Add 2 to both sides.

• Subtract 8 from both sides.

• Divide both sides by 2.

What is the solution to the inequality 2x ≥ 8?

• x ≥ 4

• x ≤ 4

• x > 4

• x < 4

What does the solution x ≥ 4 represent in the context of the function's domain?

• The function is defined for all x less than 4.

• The function is defined for all x greater than or equal to 4.

• The function is defined for all x equal to 4.

• The function is undefined for all x greater than 4.

Which of the following is another way to express the domain of the function?

• x = 4

• x < 4

• x > 4

• x ≥ 4

What is the final conclusion about the domain of the function f(x) = √(2x - 8)?

• The domain is all real numbers.

• The domain is all real numbers less than 4.

• The domain is all real numbers greater than or equal to 4.

• The domain is all real numbers greater than 4.