Exploring the Composition of Functions

This video tutorial explains the concept of function composition, a continuation of operations on functions. It introduces the notation and definition of composition, using an open circle symbol. The video provides two examples: F composed with G and G composed with F, demonstrating the step-by-step process of substituting one function into another. It emphasizes that composition is not commutative, meaning the order of functions matters. The tutorial concludes with a summary of key points and encourages viewers to practice the concept.

What is the symbol used to denote the composition of functions?

• A plus sign

• A minus sign

• A multiplication sign

• An open circle

In the composition of functions, what does the open circle symbol represent?

• Composition

• Multiplication

• Subtraction

• Addition

If F(x) = x^2 + 3x - 1 and G(x) = 2x - 5, what is F composed with G of X?

• 2x^2 + 6x - 7

• 4x^2 - 14x + 9

• x^2 + 3x - 1

• 2x - 5

When simplifying F composed with G of X, what is the first step?

• Multiply F and G

• Replace G(x) with its expression

• Add F and G

• Subtract G from F

What is the result of simplifying (2x - 5)^2?

• 4x^2 + 20x + 25

• 4x^2 - 20x + 25

• 4x^2 - 10x + 25

• 4x^2 - 20x - 25

What is the simplified form of F composed with G of X?

• 2x^2 + 6x - 7

• 4x^2 - 14x + 9

• x^2 + 3x - 1

• 2x - 5

If F(x) = x^2 + 3x - 1 and G(x) = 2x - 5, what is G composed with F of X?

• 2x - 5

• 4x^2 - 14x + 9

• x^2 + 3x - 1

• 2x^2 + 6x - 7

When simplifying G composed with F of X, what is the first step?

• Replace F(x) with its expression

• Subtract F from G

• Multiply G and F

• Add G and F

What is the simplified form of G composed with F of X?

• 4x^2 - 14x + 9

• 2x^2 + 6x - 7

• x^2 + 3x - 1

• 2x - 5

Why are F composed with G and G composed with F not the same?

• Because composition is distributive

• Because composition is not commutative

• Because composition is associative

• Because composition is commutative