Operations of Functions (Precalculus - College Algebra 5)

How to Add, Subtract, Multiply, and Divide Functions and find the resulting domain.

[resident]

hey leonard, i like coming back to your videos to watch you teach. seeing that youre doing precalc/college alg makes me happy. to help understand the higher math stuff, a strong base in the early stuff is extraordinarily helpful. youre becoming a huge thing in the undergrad stem world. i hear people say watch your videos all the time in calc 1-3. your teaching style resonates so much that youre pretty much teaching a new generation of scientists, mathematicians, engineers, etc. thanks for everything you do.

[wrongnumberofficial]

2024/9/15 and these videos are really teaching me, i will try to put comment once in a while to show my progress, and man you are saving my ass

[logohs]

Just bought a bunch of your decals from your store! I got the red and gold ones since I'm an ISU Cyclone. Just wanted to say thanks for everything you do. You have helped me tremendously in my journey to becoming an engineer.

[briangale]

When it comes to learning calculus, the quality of the teacher is paramount. Professor Leanard is the best math teacher.

[mercantilism]

I watched and took notes of your videos from 1 to 5 within a day. Everything is explained in a fairly easy way. Thank you

[BoZhaoengineering]

These are must have things before calculus class and algebra based physics class. I remember when I relearn physics, the difficulties come from mathematics. Nice.

[graceturnbull]

In highschool I was always wanting to know the "whys" in math and I had great teachers but they wouldn't always be able to or willing to delve into the "whys". I'm really grateful for how much you emphasize understanding why we need the "whys" to feel concrete about following the have tos.

[VincentBladen]

Thank you so much Sir. I am an international student who is going to attend college in the US.I am really lack of maths knowledge since I didn't understand most of the maths lessons that I was taught in my country government school. But by watching your videos, I can recall most of the things that I forgot and I really love the way you teaches which includes jokes and perspectives from the student that help me easy to understand your lessons. Right now, I am confident enough to take maths courses at the college that are waiting ahead.

[Mark-nmsm]

The more I get my hands dirty with advanced material in college the more I realise how much important it is to have strong foundations. Unfortunately i have not grasped intuitivally many concepts from pre-calc and calc 1 like derivatives and integrals and math has a way to humble you when you are reading up on Machine learning or cryptography on a slightly deeper level and you feel like the dumbest person in the world.
I like teachers with passion like prof leonard that make the video come to life. Ty for the free content you are providing to us all

[joey]

Your content is critical for me doing well in my math courses! Thank you professor! You make math very intriguing!

[philosophertiger]

Thankyou for helping me get ready for Computer science.

[Abubakarmangrio-jvek]

Hey leonard. Hope you will be doing well. I am writing this for you that 2-3 months ago I didnt know anything clearly about math. One of my friends suggest you're channel so i started watching you're vedios. I completed your intermediate algebra playlist and doing pre calculus. And now i can do most of the problems just b/c of your. Love from Pakistan.❤

[georgesadler]

Professor Leonard, thank you for a solid explanation and smooth analysis on the Operations of Functions in classic Precalculus and College Algebra. I am currently reviewing Precalculus, Trigonometry, Calculus, Linear Algebra and Differential Equations.

[WaBCIPa]

For those who don't understand why we keep the domain of previous functions even though the domain seems to be cancelled out, I think I've figured out what the problem is. In the division we're assuming that denominators are not equal to zero, because if you put 2/3 instead of x you get ((4/3 + 3)/0) / (8/3/0) which is nonsense. So when we're doing the division we're assuming that previous denominators still cannot be 0, and this carries to the new function even though it seems like there is no problem anymore. If this was independent function then yeah there would be no problem, but since we got it by dividing two other function we have to consider the domains of those functions. I hope I got it right

[DanaNourie]

I had mistakingly glossed over domains in the past. Love these videos!

[iyalodeolajubu]

your work can help me become a pilot engineer. thank you so much.

[seraknepp]

Thank you! I spent hours/days/months finding you. You are really helping me understand everything. It is so hard to remember every step and the way you are doing these videos has really helped me. I was so stressed. So my biggest thanks to you! you are saving so many people with the way you do these videos!! THANK YOU, THANK YOU, THANK YOOOOU!!

[abingeorge]

This man is a genius, I only wish I found this in High school

[forrestsmith]

Hi Professor Leonard, Is there a book that you use that we might follow along with. I ask because I'd like to be able to have more problems to practice with from each video and check them. Thanks in advance for your help. And thanks for what you're doing for us.

[angiecastillo]

you are the best professor, thanks you for saving me