Composite Functions and Their Properties

The video tutorial explains composite functions, which are functions of functions. It introduces two functions, f(x) = 2x - 1 and g(x) = 3x - 2, and demonstrates how to form the composite function f(g(x)). The tutorial provides a step-by-step calculation of f(g(x)), resulting in the expression 6x - 5. The video concludes with a summary of the composite function process.

What is a composite function?

• A function of a function

• A function that multiplies two numbers

• A function that divides two numbers

• A function that adds two numbers

What is the expression for f(x) in the given example?

• x - 2

• 2x - 1

• 2x + 1

• 3x - 2

What is the expression for g(x) in the given example?

• x + 2

• 2x + 3

• 3x - 2

• 2x - 1

How is the composite function f(g(x)) written?

• f + g(x)

• f(g(x))

• f * g(x)

• f - g(x)

What is the first step in forming the composite function f(g(x))?

• Substitute g(x) into f(x)

• Multiply the functions

• Subtract the functions

• Add the functions

What expression do you substitute for x in f(x) when forming f(g(x))?

• x - 3

• 3x - 2

• x + 2

• 2x - 1

What is the expression for f(g(x)) after substituting g(x) into f(x)?

• 2(3x - 2) - 1

• 3(2x - 1) + 2

• 2x - 1 + 3x - 2

• 3x - 2 - 2x + 1

What is the result of expanding 2(3x - 2) in the composite function?

• 6x - 4

• 6x + 4

• 3x - 4

• 3x + 4

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

• 6x - 5

• 5x + 6

• 5x - 6

• 6x + 5

What operation is performed after expanding the expression in f(g(x))?

• Addition

• Subtraction

• Division

• Multiplication