Function Composition and Evaluation

The video tutorial explains how to express the composition of functions g(f) and f(g) as sets of ordered pairs. It provides step-by-step solutions to two problems, demonstrating the process of identifying inner and outer functions and mapping values accordingly. The tutorial also addresses common errors and offers practice with a second set of problems, emphasizing the importance of understanding function composition.

What is the main focus of the video tutorial?

• Solving quadratic equations

• Graphing linear functions

• Expressing g(f) and f(g) as sets of ordered pairs

• Understanding matrix operations

In the first problem, what is the initial step to find g(f)?

• Calculate the range of f

• Begin with the inner function

• Identify the domain of g

• Start with the outer function

What is the result of g(4) in the first problem?

• 2

• 6

• 4

• 10

What is the result of g(5) in the first problem?

• 9

• 5

• 3

• 1

In the first problem, what is the result of g(-3)?

• -3

• -10

• 3

• 0

What is the result of g(1) in the first problem?

• 1

• 4

• 6

• 5

What is the result of g(0) in the first problem?

• 6

• 1

• 0

• 5

What is the result of g(2) in the first problem?

• 5

• 6

• 2

• 1

How do you determine f(g) in the first problem?

• By starting with the inner function

• By using the domain of f

• By starting with the outer function

• By using the range of g

What is the value of f(1) in the first problem?

• 4

• 6

• 5

• 1