Algebraic Operations and Domain in Functions

This video tutorial by Denny Hendayani on the MATLAB channel covers the composition of functions, focusing on algebraic operations such as addition, subtraction, multiplication, and division. It explains the properties of these operations, including commutative and associative properties, and how to determine the domain of functions resulting from these operations. The video is structured into three main parts, each addressing a specific aspect of algebraic operations on functions.

What is the result of adding two functions F(x) and G(x)?

• F(x) + G(x)

• F(x) - G(x)

• F(x) * G(x)

• F(x) / G(x)

Which of the following is a requirement for dividing two functions?

• The divisor function must be greater than zero.

• Both functions must be equal.

• The dividend function must be zero.

• The divisor function must not be zero.

What property allows the order of addition to be changed without affecting the result?

• Transitive

• Commutative

• Distributive

• Associative

Which property allows grouping of functions in addition to be changed?

• Identity

• Distributive

• Associative

• Commutative

How is the domain of the sum of two functions F and G determined?

• Product of the domains of F and G

• Difference of the domains of F and G

• Union of the domains of F and G

• Intersection of the domains of F and G

What is the domain of a function involving a square root?

• The entire set of real numbers

• Values where the expression inside the root is non-negative

• Values where the expression inside the root is negative

• Values where the expression inside the root is zero

When multiplying two functions, how is the domain determined?

• Union of the domains of both functions

• Intersection of the domains of both functions

• Product of the domains of both functions

• Difference of the domains of both functions

What must be true for the domain of a function resulting from division?

• The divisor function must be negative.

• Both functions must be positive.

• The dividend function must be zero.

• The divisor function must not be zero.

What is the domain of the function F(x) = 3x^2?

• All non-zero numbers

• All negative numbers

• All positive numbers

• All real numbers

What is the domain of the function G(x) = 1/(x-3)?

• All positive numbers

• All negative numbers

• All real numbers

• All real numbers except 3