Decomposing Functions: Inside and Outside

This video tutorial explains how to decompose composite functions into their outside and inside parts. It provides several examples, including functions like 1 over something, sine, square root, squared, 1 over square root, tangent, and cosine. Each example demonstrates how to identify the outside function and the inside function, helping students understand the structure of composite functions.

What is the purpose of decomposing composite functions?

• To eliminate the function

• To change the function's domain

• To make the function more complex

• To simplify the function for easier computation

What is the main goal of writing composite functions in a table format?

• To eliminate the function

• To clearly separate and identify the outside and inside functions

• To make the function more complex

• To change the function's range

In the decomposition of 1 over something, what is the inside function?

• x + 1

• 1 over x

• x squared

• sine of x

Which function is used as the outside function in the decomposition of 1 over something?

• y equals 1 over u

• y equals cosine u

• y equals u squared

• y equals sine u

What is the outside function when decomposing the sine of something?

• y equals sine u

• y equals cosine u

• y equals tangent u

• y equals u squared

What is the argument of the sine function in its decomposition?

• three x squared minus x plus one

• tangent of x

• x plus one

• 2x

In the decomposition of the square root function, what is the inside function?

• tangent of x

• sine of x

• x plus one

• three x squared minus x plus one

Which expression represents the inside function for the square root decomposition?

• three x squared minus x plus one

• tangent of x

• x plus one

• sine of x

What is the outside function for something squared?

• y equals square root of u

• y equals u squared

• y equals sine u

• y equals 1 over u

What is the inside function for the decomposition of something squared?

• cosine of x

• sine of x

• tangent x

• x plus one