## Composition of Functions

#### Aligned To Common Core Standard:

**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)= x^{2}
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

- Function Composition
Step-by-step Lesson- We split the problem into inner and outer
functions to play around with.

- Guided Lesson
- We work on finding the function rule. This really baffles kids
at first.

- Guided Lesson Explanation
- This is mostly a plug and chug set of problems. Question two does
require a little more work.

- Practice Worksheet
- Evaluate the composition of all the mixed functions. They all
follow a similar pattern.

- Matching Worksheet
- I tried to throw a few extra setups with exponents in here.

#### 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) = x
^{2}+ 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.