Composition of Functions

June 29, 2022

Composition of Functions

For the function g defined above, a, is a constant and g(4) = 8. What is the value of g(-4)?

g(x) = ax2 + 24

These Do Nows are all questions from the SAT's or ACT's. You are not expected to solve them, but try your best and then we will discuss as a class.

Do Now

Today you will find the composition of two functions by using the output of one function as the input of the other.

OBJECTIVE

Composing multiple functions allows you to evaluate how multiple functions impact a starting input value. For example, department stores often have multiple sales going on at the same time. You can use composition of functions to find the best sale

PURPOSE

• Combining functions where the output (range) of one function becomes the input (domain) of another.
• Inner parentheses are done first:
• f(g(x)) means the ouput of g(x) is the input of f(x)
• g(f(x)) means the output of f(x) is the input of g(x)

Composition of Functions

Example

Given f(x) = x + 4 and g(x) = 2x.Find f(g(2)) and g(f(2))

Your Turn!

Given f(x) = x - 5 and g(x) = 3x, Find f(g(6))Find g(f(6))

(f 𐩒 g)(x)

• The notation for composition of functions is:

• We say "f composed with g of x" or "f of g of x"

Composition Notation

Example

Given the functions f(x) = 5x and g(x) = x2 + 1, find (f 𐩒 g)(x).

Your Turn!

Given the functions f(x) = 5x and g(x) = x2 + 1, find (g 𐩒 f)(x).

Two nights ago, Zoé was found dead at Sewickley Academy. It is your job to determine who committed the crime, where it happened, and what was the murder weapon.

The Mystery of Breakthrough...

There are 10 cards around the hallway with practice problems. The correct answer will lead you one step closer to solving the mystery

The Mystery of Breakthrough...

Library

What?

Where?

Who?

Four square game

Basketball

Spirit Sticks

Cafeteria

Maddy

Mickey

Commons

Gym

Imane

Julianne

Heather

Margin

Given h(a) = -2a3 + 3a and g(a) = a - 3. Find h(g(-1)).

Exit Slip