Function Composition and Evaluation

The video tutorial explains how to find composite function values, specifically F(G(2)) and G(F(2)), using given functions F(x) = x^2 + 5 and G(x) = 6x - 15. It demonstrates the step-by-step process of calculating these values by substituting and following the order of operations. The tutorial emphasizes the importance of the order in which functions are composed, as it affects the final result.

What are the given functions f(x) and g(x) in the video?

• f(x) = 2x + 5 and g(x) = 6x - 10

• f(x) = x^2 + 5 and g(x) = 6x - 15

• f(x) = x^2 + 10 and g(x) = 6x - 5

• f(x) = x^2 - 5 and g(x) = 6x + 15

What is the first step in finding f(g(2))?

• Calculate f(2)

• Calculate g(2)

• Calculate f(g(x))

• Calculate g(f(x))

What is the value of g(2)?

• -3

• 12

• 3

• 15

What is the result of substituting g(2) into f(x)?

• -3

• 14

• 9

• 0

What is the composite function value f(g(2))?

• -3

• 9

• 14

• 39

What is the first step in finding g(f(2))?

• Calculate g(2)

• Calculate g(f(x))

• Calculate f(g(x))

• Calculate f(2)

What is the value of f(2)?

• 9

• 14

• 4

• 5

What is the result of substituting f(2) into g(x)?

• 15

• 54

• 24

• 39

Why is it important to pay attention to the order of composition?

• Because the results of f(g(x)) and g(f(x)) can be different

• Because it affects the speed of calculation

• Because it changes the functions used

• Because it simplifies the process

What is the composite function value g(f(2))?

• -3

• 14

• 39

• 9