Combination of Functions: (f+g)(x), (f-g)(x), (fg)(x), (f/g)(x)

in MES Science3 months ago (edited)

In this video I go over the definitions and notations involved in combining two different functions. What I mean by combining functions, I mean adding, subtracting, multiplying and dividing two functions.


Watch video on:

Download video notes: https://1drv.ms/b/s!As32ynv0LoaIiOYm_2RuYzYLaNsaMQ?e=vpcgVY


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:

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

Join my forums!

Follow along my epic video series:


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

Browser extension recommendations:


Combination of Functions.PNG

Combination of Functions

image.png

Algebra of Functions

Let f and g be functions with domains A and B.

Then the functions f + g, f – g, fg, and f/g are defined as follows:

  • (f + g)(x) = f(x) + g(x) with domain = A ∩ B
  • (f – g)(x) = f(x) – g(x) with domain = A ∩ B
  • (fg)(x) = f(x)g(x) with domain = A ∩ B
  • (f/g)(x) = f(x)/g(x) with domain = {x ϵ A ∩ B|g(x) ≠ 0}
    • ϵ = element of or inside.
    • | = except
    • f/0 is not defined.

Example

image.png

Solution

image.png

image.png

image.png

image.png

image.png