Exploring Function Operations and Composition

This video tutorial covers function operations in algebra, including addition, subtraction, multiplication, and division of functions. It explains the notation used for these operations and provides example problems to illustrate how to perform them. The tutorial also discusses the domain of functions and introduces the concept of composition of functions, where one function is plugged into another. The video aims to make these concepts accessible and easy to understand for students.

What are the four basic operations that can be performed on functions?

• Subtraction, Multiplication, Division, Integration

• Addition, Multiplication, Integration, Differentiation

• Addition, Subtraction, Integration, Differentiation

• Addition, Subtraction, Multiplication, Division

What is the result of adding the functions f(x) = x^2 - 4x and g(x) = 2x - 7?

• x^2 - 6x - 7

• x^2 - 2x - 7

• x^2 - 6x + 7

• x^2 - 2x + 7

What is the domain of the function f(x) = x^2 - 4x?

• All real numbers

• x > 0

• x < 0

• x ≠ 0

When subtracting the functions f(x) = x^2 - 4x and g(x) = 2x - 7, what is the result?

• x^2 - 6x + 7

• x^2 - 2x - 7

• x^2 - 6x - 7

• x^2 - 2x + 7

What is the result of multiplying the functions f(x) = x^2 - 4x and g(x) = 2x - 7?

• 2x^3 - 8x^2 - 28x

• 2x^3 - 15x^2 + 28x

• 2x^3 - 8x^2 + 28x

• 2x^3 - 15x^2 - 28x

What is the domain of the function f(x) = 2x - 7?

• All real numbers

• x < 0

• x > 0

• x ≠ 0

What is the result of dividing the functions f(x) = x^2 - 4x and g(x) = 2x - 7?

• (x^2 - 4x) / (2x - 7)

• (x^2 - 4x) / (x - 7)

• (x^2 - 4x) / (2x + 7)

• (x^2 - 4x) / (x + 7)

What does the notation f(g(x)) represent?

• The difference of f and g

• The composition of f and g

• The product of f and g

• The sum of f and g

Given f(x) = 2x - 3 and g(x) = x^2 - 4x, what is f(g(x))?

• 2x^2 - 4x + 3

• 2x^2 - 4x - 3

• 2x^2 - 8x + 3

• 2x^2 - 8x - 3

Given f(x) = x^2 - x + 1 and g(x) = √(x + 2), what is g(f(x))?

• √(x^2 - x + 3)

• √(x^2 - x + 4)

• √(x^2 - x + 1)

• √(x^2 - x + 2)