## Invertible Functions

#### Aligned To Common Core Standard:

**Building Functions** - HSF-BF.B.4d

What are Invertible Functions?
If you think that mathematical functions are difficult and they make you anxious, then don't worry. Here, we will help you understand everything that scares you in the simplest terms.
Just like everything has an opposite, like day and night, hot and cold, shiny and dull, functions also have opposites or inverses that are known as invertible. Not every function has an inverse.
In the most general sense, functions that reverse each other are known as inverses. A function is known as invertible only your input has a unique output. To clarify, each output is paired with exactly one input so that when you reverse the input, it will still be a function.
Consider a function; f(y)= 4y + 6
Then, the inverse of the function will be f - 1(y)= y^{-6/4} These worksheets and lessons look at special functions that are unique in that each input has a unique output.

### Printable Worksheets And Lessons

- Inverse Functions
Step-by-step Lesson-See if you can find the inverse of the given
function.

- Guided Lesson
- These problems have several steps for you to run through to get
them prepared for the final step.

- Guided Lesson Explanation
- Swapping out the x and y variables help here a lot.

- Practice Worksheet
- You will find all four standard formats of functions to work with
here.

- Matching Worksheet
- Don't forget about the notation used for an inverse of a function.

#### Homework Sheets

We start with very deliberate values for f(x).

- Homework 1 - Swap the x and y variables to create the inverse relation will be the set of ordered pairs.
- Homework 2 - Divide both sides by 5: x+3 = 5y and swap sides.
- Homework 3 - Find the inverse of the function: f(x)=x+3/x

#### Practice Worksheets

We introduce multiple operations in these problems.

- Practice 1 - Determine the inverse of this function. Is the inverse also a function?
- Practice 2 - What is the inverse of the function f(x) = 5x-7
- Practice 3 - These are more about noticing a pattern.

#### Math Skill Quizzes

These function table questions might take a little extra time.