Explanation

A function is a rule that takes an input and gives an output.

Example:
f(x) = x + 2
If x = 3, then f(3) = 5

Composing functions means using one function inside another.

Think of it like:

• First function → second function

Example:
f(x) = x + 2
g(x) = x × 3

g(f(x)) means:

1. Start with x

2. Apply f(x): x + 2

3. Apply g(x): (x + 2) × 3

So:
g(f(x)) = 3(x + 2)

Quiz: Composing Functions

1. What does it mean to compose functions?

2. If f(x) = x + 1, what is f(4)?

3. If g(x) = x × 2, what is g(5)?

4. If f(x) = x + 1 and g(x) = x × 2, what is g(f(3))?

5. True or False: You always apply the outside function first.

Answer Key

1. Using one function inside another

2. 5

3. 10

4. 8

5. False