Operations with Functions and Domains

The video tutorial explains how to perform operations on two functions, f(x) and g(x), including addition, subtraction, multiplication, and division. It begins by expanding f(x) from its factored form and then applies each operation step-by-step, highlighting the importance of parentheses in subtraction and the domain considerations in division. The tutorial emphasizes the need to consider the domain of the resulting functions, especially when division by zero could occur.

What is the expanded form of f(x) if f(x) is given as (x + 2)^2?

• x^2 + 2x + 2

• x^2 + 2x + 4

• x^2 + 4x + 4

• x^2 + 4x + 2

When adding two functions, why is it important to use parentheses?

• To simplify the expression

• To avoid errors in subtraction

• To make the expression look neat

• To ensure correct order of operations

What is the result of f(x) + g(x) if f(x) = x^2 + 4x + 4 and g(x) = 2 - 3x?

• x^2 + 7x + 6

• x^2 + x + 6

• x^2 + 4x + 2

• x^2 + x + 2

What is the domain of the sum of two functions if both have domains of all real numbers?

• All integers

• All positive numbers

• All real numbers

• All negative numbers

What is the result of f(x) - g(x) if f(x) = x^2 + 4x + 4 and g(x) = 2 - 3x?

• x^2 + x + 2

• x^2 + 7x + 2

• x^2 + 4x + 2

• x^2 + 7x + 6

How many products are formed when multiplying f(x) = x^2 + 4x + 4 by g(x) = 2 - 3x?

• Seven

• Four

• Five

• Six

What is the leading term of the product f(x) * g(x) if f(x) = x^2 + 4x + 4 and g(x) = 2 - 3x?

• 2x^2

• -3x^2

• 2x^3

• -3x^3

What is the domain of the product of two functions if both have domains of all real numbers?

• All integers

• All negative numbers

• All positive numbers

• All real numbers

What must be excluded from the domain of f(x) / g(x) if g(x) = 2 - 3x?

• x = 0

• x = 2/3

• x = 3/2

• x = -2/3

How is the domain of the quotient of two functions determined?

• By including only positive values

• By including only negative values

• By excluding values that make the denominator zero

• By finding the union of the domains