QUICK LINKS


Function Composition Calculator

QUICK LINKS


Function Composition Calculator

CALCULATOR
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Function Composition Calculator

Functions:
Evaluate:

or

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.
Now, replace every on the right side with the function you entered in for :
We have some questions for you! Help us out through this
INTRO
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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.

Start with

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
sections to learn more about functions and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

KEY STEPS
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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.

Step 2. Simplify the expression.

(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
β€” Evaluating Function Composition (Variable Input)
PRACTICE
β€” Evaluating Function Composition (Variable Input)
LESSON
β€” Evaluating Function Composition (Numerical Input)
PRACTICE
β€” Evaluating Function Composition (Numerical Input)
CONCLUSION
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