Function Decomposition and Composition

This video tutorial explains how to decompose a function into two functions, f(x) and g(x), such that h(x) = f(g(x)). The instructor provides four examples: a square root function, a rational function, an absolute value function, and a polynomial function. Each example demonstrates how to identify the inside and outside functions, g(x) and f(x), respectively. The video concludes with a summary of the decomposition process.

What is the main idea behind function decomposition?

• Breaking a function into two simpler functions

• Combining two functions into one

• Finding the derivative of a function

• Solving a function for x

In the function h(x) = √(7x + 5), what is the inside function g(x)?

• 5x + 7

• x^2

• √x

• 7x + 5

For the function h(x) = √(7x + 5), what is the outside function f(x)?

• x + 5

• √x

• 7x + 5

• x^2

In the function h(x) = 1/(x + 3), what is the outside function f(x)?

• 3x + 1

• x + 3

• 1/x

• x^2

For the function h(x) = 1/(x + 3), what is the inside function g(x)?

• x^2

• x + 3

• 1/x

• 3x + 1

In the function h(x) = |3x + 2|, what is the inside function g(x)?

• x + 3

• x^2

• |x|

• 3x + 2

For the function h(x) = |3x + 2|, what is the outside function f(x)?

• x^2

• |x|

• x + 3

• 3x + 2

In the function h(x) = (2x^3 + 7x - 3)^4, what is the inside function g(x)?

• 7x + 3

• x^3

• x^4

• 2x^3 + 7x - 3

For the function h(x) = (2x^3 + 7x - 3)^4, what is the outside function f(x)?

• x^3

• x^4

• 7x + 3

• 2x^3 + 7x - 3

What is the purpose of identifying inside and outside functions in decomposition?

• To simplify the process of differentiation

• To find the inverse of a function

• To solve equations faster

• To understand the structure of complex functions