In my earlier video, I showed how you can combine functions but only algebraic terms such as division and subtraction. But that is not the only way to combine functions; in this video I show how you can combine multiple functions by the procedure known as composition. I also go through an example to illustrate the notation and concept of composition of functions.

Watch video on:

• 3Speak:
• DTube: https://d.tube/#!/v/mes/QmWbbSPYjcSThvA578ijGyyRjXcVcUqVbmwH2791NPkoje
• BitChute: https://www.bitchute.com/video/vUvVQzHt0OJF/
• YouTube: https://youtu.be/8HJE47q7-pA

Download video notes: https://1drv.ms/b/s!As32ynv0LoaIiOUfoeysY4sSmYzyXg?e=UM4ZDg

View Video Notes Below!

Download these notes: Link is in video description.
View these notes as an article: https://peakd.com/@mes
Subscribe via email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate
Buy MES merchandise! https://mes.fm/store
More links: https://linktr.ee/matheasy

Reuse of my videos:

• Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.

Fight back against censorship:

• Bookmark sites/channels/accounts and check periodically
• Remember to always archive website pages in case they get deleted/changed.

Recommended Books:

• "Where Did the Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook

Subscribe to MES Truth: https://mes.fm/truth

Join my forums!

• Hive community: https://peakd.com/c/hive-128780
• Reddit: https://reddit.com/r/AMAZINGMathStuff
• Discord: https://mes.fm/chatroom

Follow along my epic video series:

• #MESScience: https://mes.fm/science-playlist
• #MESExperiments: https://peakd.com/mesexperiments/@mes/list
• #AntiGravity: https://peakd.com/antigravity/@mes/series
  -- See Part 6 for my Self Appointed PhD and #MESDuality breakthrough concept!
• #FreeEnergy: https://mes.fm/freeenergy-playlist
• #PG (YouTube-deleted series): https://peakd.com/pg/@mes/videos

---

NOTE #1: If you don't have time to watch this whole video:

• Skip to the end for Summary and Conclusions (if available)
• Play this video at a faster speed.
  -- TOP SECRET LIFE HACK: Your brain gets used to faster speed!
  -- MES tutorial: https://peakd.com/video/@mes/play-videos-at-faster-or-slower-speeds-on-any-website
• Download and read video notes.
• Read notes on the Hive blockchain #Hive
• Watch the video in parts.
  -- Timestamps of all parts are in the description.

Browser extension recommendations:

• Increase video speed: https://mes.fm/videospeed-extension
• Increase video audio: https://mes.fm/volume-extension
• Text to speech: https://mes.fm/speech-extension
  --Android app: https://mes.fm/speech-android

Composition of Functions

Definition

Given two functions f and g, the composite function f◦g (also called the composition of f and g) is defined by:

(f◦g)(x) = f(g(x))

Domain

The domain of f◦g is the set of all x in g such that g(x) is in the domain of f.

In other words, (f◦g)(x) is defined whenever both g(x) and f(g(x)) are defined.

Notes

• From the example, in general f◦g ≠ g◦f
• The notation mean f◦g means the function g is applied first and then f is applied second.