Exploring Composition of Functions

This video tutorial covers the concept of function composition, explaining different notations and demonstrating the process through examples. It emphasizes the importance of order in composition and shows how to express functions in terms of X using composition. The video provides step-by-step solutions for specific examples, illustrating how to simplify and evaluate compositions efficiently.

What is the preferred notation for composition of functions according to the video?

• G of F of x

• G(F(x))

• F of G of x

• F(G(x))

In the first example, what is the value of G(2)?

• 12

• 11

• 13

• 10

What is the final result of f(g(2)) in the first example?

• 19

• 22

• 20

• 21

In the second example, what is the value of f(2)?

• 4

• 5

• 3

• 2

What is the final result of g(f(2)) in the second example?

• 20

• 21

• 19

• 18

When writing f(g(x)), what is the expression for g(x)?

• x^2 + 3x + 1

• x^2 + 4x + 1

• x^2 + 5x + 1

• x^2 + 2x + 1

What is the simplified form of f(g(x))?

• 2x^2 + 6x + 1

• 2x^2 + 7x + 1

• 2x^2 + 8x + 1

• 2x^2 + 5x + 1

When writing g(f(x)), what is the expression for f(x)?

• 2x - 1

• 2x - 4

• 2x - 2

• 2x - 3

What is the simplified form of g(f(x))?

• 4x^2 + 2x - 2

• 4x^2 + 3x - 1

• 4x^2 + 2x - 1

• 4x^2 + 3x - 2

What is the final result of g(f(2)) when calculated directly?

• 18

• 21

• 19

• 20