Exploring Operations on Functions

The video tutorial covers operations on functions, including addition, subtraction, multiplication, and division. It explains how to perform these operations and provides examples for each. The tutorial also discusses domain considerations, especially when dividing functions. The video concludes with a preview of the next topic: composition of functions.

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

• F / G

• F * G

• F + G

• F - G

Which of the following is NOT true about the addition of functions?

• It is similar to adding polynomial expressions.

• It uses the distributive property.

• It is denoted as F + G of X.

• It results in a new function.

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

• To ensure the correct order of operations.

• To avoid sign errors.

• To apply the distributive property.

• To simplify the expression.

What is the result of subtracting G(x) from F(x) if F(x) = x^2 - 3 and G(x) = 2x + 5?

• x^2 + 2x - 8

• x^2 - 2x + 2

• x^2 + 2x + 2

• x^2 - 2x - 8

What is the result of multiplying two functions F and G?

• F - G

• F / G

• F * G

• F + G

If F(x) = x^2 - 3 and G(x) = 2x + 5, what is F * G of X?

• 2x^3 - 5x^2 + 6x + 15

• x^2 + 2x + 2

• 2x^3 + 5x^2 - 6x - 15

• x^2 - 2x - 8

What must be true about the denominator when dividing two functions?

• It must not be zero.

• It must be a polynomial.

• It can be zero.

• It must be a constant.

If F(x) = x^2 - 3 and G(x) = 2x + 5, what is F / G of X?

• (2x + 5) / (x^2 - 3)

• (x^2 - 3) / (2x + 5)

• (2x - 5) / (x^2 + 3)

• (x^2 + 3) / (2x - 5)

What is the domain of the function F / G of X if F(x) = x^2 - 3 and G(x) = 2x + 5?

• All real numbers except x = 5/2

• All real numbers except x = 0

• All real numbers

• All real numbers except x = -5/2

What is the next topic to be discussed after operations on functions?

• Inverse functions

• Rational functions

• Polynomial functions

• Composition of functions