Using operations to combine rational functions

The video tutorial explains how to perform basic operations on two functions, F and G, including addition, subtraction, multiplication, and division. It demonstrates the process of finding common denominators for addition and subtraction, multiplying fractions for multiplication, and using reciprocals for division. The tutorial emphasizes the importance of ensuring that the denominator is not zero during division.

What is the first step in adding two functions like F(x) = 1/x and G(x) = 1/x^2?

• Divide the functions

• Subtract the functions

• Find a common denominator

• Multiply the numerators

When subtracting two functions, what must be done to the denominators?

• They must be divided by each other

• They must be multiplied by each other

• They must be added together

• They must be made the same

How do you multiply two functions like F(x) = 1/x and G(x) = 1/x^2?

• Subtract the numerators

• Multiply the numerators and denominators

• Add the numerators

• Divide the numerators

What is the result of dividing F(x) = 1/x by G(x) = 1/x^2?

• x

• 1/x

• 1/x^3

• x^2

Why is it important to ensure the denominator is not zero when dividing functions?

• To make the numerator zero

• To ensure the functions are equal

• To simplify the expression

• To avoid undefined results