STUDENT
TEACHER

Function Composition Calculator

STUDENT
TEACHER

Function Composition Calculator

# Function Composition

CALCULATOR

## Function Composition Calculator

Functions:
Evaluate:

or
We have some questions for you! Help us out through this
INTRO
Function composition (or composition of functions) usually looks like or , which both read as " of of ."
To help us better understand function composition, let’s imagine we want to buy some merch, and we can use two coupons to bring down the original price.
When we apply the first coupon, we get an initial discounted price. Then, when we apply the second coupon we get our final discounted price.

This is like how in function compositions, the output of the inside function becomes the input of the outside function to produce the final output.
And, notice that the order in which we use the coupons affects the final price! This is why we always have to work from the inside out to guarantee the correct answer when we evaluate function compositions.

### What is a function?

Functions define the relationships between inputs and outputs. For a review on how functions work and how to evaluate them, make sure to check out our lesson!
Check out our
Calculator
or explore our
Lesson
and
Practice

KEY STEPS

## How to Evaluate Function Composition

When a is in the second set of parentheses.
Ex.

### Step 1. Plug in the inside function wherever the variable shows up in the outside function.

The inside function is the input for the outside function.

### (optional) Step 3. Plug in the input.

Plug in the input everywhere the variable shows up in the composite function.

### (optional) Step 4. Calculate the output.

Use order of operations (PEMDAS) to calculate the output.
LESSON
Evaluating Function Composition (Variable Input)
PRACTICE
Evaluating Function Composition (Variable Input)
LESSON
Evaluating Function Composition (Numerical Input)
PRACTICE
Evaluating Function Composition (Numerical Input)
CONCLUSION
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