Master Composing two functions linear and quadratic

The video tutorial explains how to compose and evaluate the composition of two functions, F and G. It covers the process of composing F of G of X and G of F of X, demonstrating how to substitute one function into another. The tutorial also includes examples of evaluating these compositions with specific values, such as 2 and -2, and emphasizes the importance of using parentheses to avoid errors. The instructor uses color coding and step-by-step explanations to clarify the process, ensuring that students understand how to handle both linear and quadratic functions in compositions.

What is the main concept behind composing two functions?

• Multiplying two functions

• Subtracting one function from another

• Evaluating one function using another function

• Adding two functions together

If F(x) = 3x and G(x) = x + 5, what is F(G(x))?

• x + 15

• 3x + 15

• 3(x + 5)

• 3x + 5

What is the simplified form of F(G(x)) if F(x) = 3x and G(x) = x + 5?

• x + 15

• 3(x + 5)

• 3x + 15

• 3x + 5

If F(x) = 3x and G(x) = x + 5, what is G(F(x))?

• 3(x + 5)

• 3x + 5

• x + 15

• 3x + 15

What is the result of evaluating F(G(2)) if F(G(x)) = 3x + 15?

• 18

• 21

• 15

• 12

What is the result of evaluating G(F(-2)) if G(F(x)) = 3x + 5?

• 0

• -2

• 1

• -1

What is the simplified form of F(G(x)) if F(x) = 3 - x and G(x) = 2x^2 + x + 5?

• 3x^2 + x + 5

• 2x^2 + x + 5

• -3x^2 - x - 5

• -2x^2 - x - 2

What is the result of evaluating F(G(2)) if F(G(x)) = -2x^2 - x - 2?

• -8

• -6

• -10

• -12

What is the result of evaluating G(F(-2)) if G(F(x)) = 2x^2 - 13x + 26?

• 58

• 54

• 60

• 56

Why is it important to use parentheses when evaluating compositions?

• To avoid calculation errors

• To make it easier to read

• To make the expression look neat

• To simplify the expression