CALCULATOR

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## Function Composition Calculator

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 $f(g(x) ) $ or $(f ∘g )(x)$, which both read as "$f $ of $g $ of $x$."

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

$f(x)$

$=$$0.5x$

$f(30)$

$=$$0.5(30)$

$=$$15 $

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!

Calculator

Lesson

Practice

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KEY STEPS

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## How to Evaluate Function Composition

When a is in the second set of parentheses.Ex. $f(g(x))$

### 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

— 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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