What is the domain of the product of a square root and reciprocal function

The video tutorial covers the domains of functions F(x) and G(x), explaining the restrictions for each. It discusses how to find the domain of F(x) by ensuring the expression under the radical is non-negative and the domain of G(x) by avoiding division by zero. The tutorial then explores the product of these functions, demonstrating how to multiply a radical by a fraction. Finally, it illustrates how to graph the domains and find their intersection, concluding that the domain of the product is from 5 to infinity.

What condition must be met for the domain of F(x) to be valid?

• x must be equal to 5

• x must be greater than or equal to 5

• x must be less than 5

• x must be a negative number

Why is x = 3 excluded from the domain of G(x)?

• Because it is greater than 5

• Because it is a negative number

• Because it makes the denominator zero

• Because it makes the numerator zero

How do you determine the domain of the product of two functions?

• By multiplying the domains of the two functions

• By adding the domains of the two functions

• By subtracting the domains of the two functions

• By finding the intersection of the domains of the two functions

What is the domain of the product F(x) * G(x)?

• All numbers greater than 3

• All numbers greater than 5

• All real numbers

• All numbers except 5

What is the result of multiplying a square root by a fraction?

• A square root of the product of the numerator and denominator

• A fraction with the square root in the denominator

• A square root of the sum of the numerator and denominator

• A fraction with the square root in the numerator