In Class 1.4, Operations with Functions, Composition of Functions Name: Algebra II, Unit 1: Functions

We can perform operations on functions just like we perform operations on numbers or expressions. Note that the domain of the new function may be different than the domain of 𝒇(𝒙) 𝒂𝒏𝒅 𝒈(𝒙).

Example: Given,𝑓 𝑥 = 5𝑥 − 6 𝑎𝑛𝑑 𝑔 𝑥 = 𝑥! − 5𝑥 + 6,determinea) 𝑓 𝑥 + 𝑔 𝑥 𝑜𝑟(𝑓 + 𝑔) (𝑥) b)𝑓 𝑥 – 𝑔 𝑥 𝑜𝑟 𝑓 − 𝑔 (𝑥)

Given,𝑓 𝑥 = 𝑥 + 2 𝑎𝑛𝑑 𝑔 𝑥 = 𝑥! − 4

c) 𝑓 𝑥 𝑔 𝑥 𝑜𝑟 𝑓𝑔 (𝑥) d)!(!)

!(!)𝑜𝑟 !

!(𝑥)

Compositionoffunctions:Whengoingshoppingatastoreinthemall,yousawanitemthatwasworth$100.However,thatitemisonsalefor20%off,andalsoeveryiteminthatstorewillhaveanother$20off.Ifyouwanttobuythatitem,wouldyoulikethecashiertotakeoff$20first,then20%ortakeoff20%first,andthen$20?Doyoucare?Think of the following functions: 𝑓(𝑥) = 𝑥 − 20%𝑥 = 0 .80𝑥

𝑔(𝑥) = 𝑥 − 20 A composition of functions is like a series of machines, for example: If 𝑓 𝑥 = 𝑥! − 3 and 𝑔 𝑥 = 2𝑥 − 5, then 𝑓(𝑔 4 ) looks like this: Recall the function machine puzzle from In Class 1: Inwhatordershouldyoustackthemachinessothatwhen6isdroppedintothefirstmachine,andallfourmachineshavehadtheireffect,thelastmachine'soutputis11?

𝑓(𝑥) = 𝑥 𝑔(𝑥) = −(𝑥 − 2)!

ℎ(𝑥) = 2 ! − 7 𝑘(𝑥) = −𝑥2

– 1

1)Solve:𝑔 𝑘 6

2)Whatshouldbethenextfunctioncompositiontogettothefinaloutputof11?

In Class 1.4, Operations with Functions, Composition of Functions Name: Algebra II, Unit 1: Functions