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## Composition of Functions

#### High School Building Functions - HSF-BF.A.1c

What is Function Composition? (in Math) Function composition in mathematics refers to an operation that uses two functions f ( ) and g ( ) and, as a result, produces another function. The result composition is written as (g º f)(x) which means g(f(x)). Let's consider an example f(x) = 5x+7 and g(x)= x2 Not to forget that "x" is only to denote the unknown formula, Here's the first step; f(x)= 5x+7, g(x)= (x)2 We first use f then apply for the result; (g x f)(x) = (5x + 7)2 Always be careful about which function comes first because if you inverse the function, the answer also gets affected. This series of worksheets and lessons will help students understand how to combine together and interact with multiple functions.

### Printable Worksheets And Lessons  #### Homework Sheets

These sheets are all about managing functions and finding the outcome of their relation.

• Homework 1 - Evaluate the inner function. Insert the answer from step 1 into outer function and evaluate further.
• Homework 2 - Plug m – 2 into f(c) and simplify.
• Homework 3 - The two functions t(x) and v(x) are defined below. t(x) = 6x – 4 v(x) = x2 + 5

#### Practice Worksheets

It's time for two functions to come together. Tell us how the marriage works out.

• Practice 1 - Evaluate the composition of functions v(t(6))
• Practice 2 - Use the defined functions to solve the end game.
• Practice 3 - Find the final value of all of the terms you are given first.

#### Math Skill Quizzes

Evaluate all of the composition of these functions.

• Quiz 1 - Use the following function rule to find f(m -2). Simplify your answer. F(c) = 7c
• Quiz 2 - Finish this quiz all the way through.
• Quiz 3 - Use everything you learned to pull this one together.