Evaluating Function Compositions

The video tutorial covers the evaluation of function compositions through examples. It begins with an introduction to example 6, where the composition of functions is evaluated. The tutorial demonstrates the step-by-step process of evaluating f(g(-1)), h(9), and h(g(0)). Each example is broken down into smaller steps, showing how to substitute values and simplify expressions. The video emphasizes the importance of understanding function compositions and provides clear explanations for each calculation.

What is the main focus of Example 6 in the video?

• Solving quadratic equations

• Evaluating compositions of functions

• Graphing linear functions

• Finding the derivative of a function

What is the first step in evaluating f(g(x))?

• Simplify the expression f(x)

• Find the derivative of f(x)

• Calculate g(x) for a specific input

• Graph the function g(x)

How is g(-1) calculated in the video?

• By squaring -1 and performing arithmetic operations

• By taking the square root of -1

• By adding 1 to the function

• By multiplying -1 by 2

What is the result of g(-1) in the video?

• 10

• 8

• 7

• 5

After finding g(-1), what is the next step?

• Find the inverse of f(x)

• Substitute the result into f(x)

• Graph the function f(x)

• Calculate f(0)

What is the value of f(8) as calculated in the video?

• 3

• 5

• 7

• 9

What is the first step in evaluating h(9)?

• Subtract 9 from 10

• Add 9 to 3

• Multiply 9 by 2

• Find the square root of 9

What is the result of h(9) in the video?

• 9

• 15

• 6

• 12

After finding h(9), what is the next step?

• Calculate j(0)

• Substitute the result into j(x)

• Find the inverse of j(x)

• Graph the function j(x)

What is the value of j(h(9)) as calculated in the video?

• 2/19

• 4/20

• 3/18

• 1/9