Domain of Functions and Operations

The video tutorial explores how to create new functions from existing ones by performing operations such as addition, subtraction, multiplication, and division on two functions, f(x) = √x and g(x) = √(9-x²). It emphasizes the importance of determining the domain of each function and finding their common domain to perform these operations. The tutorial provides a step-by-step guide to calculating the domains and explains the restrictions when dividing functions.

Why is it important to consider the common domain when combining functions?

• To avoid using any mathematical operations.

• To simplify the functions.

• To make the functions look more complex.

• To ensure the operations are valid for all values.

What is the domain of the function f(x) = √x?

• From -∞ to ∞

• From 0 to ∞

• From -3 to 3

• From -9 to 9

How is the domain of g(x) = √(9 - x²) determined?

• By setting 9 - x² > 0

• By setting 9 - x² ≥ 0

• By setting x² - 9 > 0

• By setting x² + 9 ≥ 0

What is the domain of g(x) = √(9 - x²)?

• From -∞ to ∞

• From -9 to 9

• From 0 to ∞

• From -3 to 3

What is the common domain for the functions f(x) = √x and g(x) = √(9 - x²)?

• From 0 to ∞

• From -∞ to ∞

• From 0 to 3

• From -3 to 3

What operation is not allowed when the denominator is zero?

• Division

• Addition

• Subtraction

• Multiplication

What is the domain for the function f(x) + g(x)?

• From -∞ to ∞

• From 0 to ∞

• From -3 to 3

• From 0 to 3

What is the domain for the function f(x) - g(x)?

• From 0 to 3

• From -∞ to ∞

• From -3 to 3

• From 0 to ∞

What is the domain for the function f(x) * g(x)?

• From -3 to 3

• From 0 to 3

• From -∞ to ∞

• From 0 to ∞

What is the domain for the function f(x) / g(x)?

• From 0 to 3

• From 0 to 3 excluding 3

• From -3 to 3

• From -∞ to ∞