Composite and Recursive Functions

The video tutorial explains how to find composite functions using two given functions, f(x) = 5x - 3 and g(x) = 2x + 9. It covers the notation for composite functions and provides detailed steps for calculating f(g(x)), g(f(x)), f(f(x)), and g(g(x)). Each calculation involves substituting one function into another and simplifying the result. The tutorial aims to help viewers understand the process of working with composite functions.

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

• 2x - 9

• 2x + 9

• 5x + 3

• 5x - 3

Which notation is used to represent the composite function f(g(x))?

• f(x) + g(x)

• f(x) * g(x)

• f(g(x))

• g(f(x))

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

• Replace f(x) with 5x - 3

• Replace g(x) with 2x + 9

• Multiply f(x) and g(x)

• Add f(x) and g(x)

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

• 25x - 18

• 4x + 27

• 10x + 3

• 10x + 42

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

• Multiply f(x) and g(x)

• Replace g(x) with 2x + 9

• Add f(x) and g(x)

• Replace f(x) with 5x - 3

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

• 4x + 27

• 25x - 18

• 10x + 3

• 10x + 42

What is the expression for f(f(x)) before simplification?

• f(5x - 3)

• g(2x + 9)

• f(2x + 9)

• g(5x - 3)

What is the simplified form of f(f(x))?

• 10x + 42

• 25x - 18

• 10x + 3

• 4x + 27

What is the expression for g(g(x)) before simplification?

• f(5x - 3)

• f(2x + 9)

• g(2x + 9)

• g(5x - 3)

What is the simplified form of g(g(x))?

• 4x + 27

• 10x + 42

• 10x + 3

• 25x - 18