Combining Functions Function Operations PLEASE READ DESCRIPTION:)

I go over combining functions through addition, subtraction, multiplication, and division. I also explain the restriction on domain of these combined functions.
Please Note:
At the end of my last example I accidentally multiplied by 1/x. I should have multiplied by x/1 as I explained and got 3x+1 as an answer.
At minute 6:04 x cannot equal -1

[profrobbob]

Sounds like they should offer my videos in their curriculum then...lol
Glad to hear that my videos were helpful and could fill in the blanks for you. Thanks for choosing my channel to learn from:)

[maxkyrus]

Such enthusiasm demonstrates what a good teacher you are! I was confused at the end as you didnt flip the 1/x but read the description and I found peace 😅. Crazy to think a video made 12 years ago still benefits today!

[Icey]

You have helped me sooo much throughout the past 4 months. Thank you prof

[emmajauernig]

Thank you so much for being such a lovely teacher :D my precalc teacher right now barely does any examples and then yells at us when we don’t understand. You are a well needed break from that stress!

[profrobbob]

You're welcome...thanks for watching and "liking" and I'm glad it was helpful for you:) Please share my channel with others too!

[profrobbob]

Thanks...Just trying to keep the viewers motivated to learn...and it helps to love what you're doing:)

[profrobbob]

You must be watching on an iPad or something that does not have Flash. This video has an annotation to correct that. When I made this video and the correction I was not aware of that issue. I need to re-record that portion of the video with my new t-shirt on that says "I'm right 98% of the time, who cares about the other 3%". Thanks for the heads up and for watching. I hope my video still helped:)

[profrobbob]

Since you were willing to seek for extra help when you needed it, I would say you are AMAZING

[FOXify]

I looked up your video because my pre-calc teacher doesn't really teach us. He makes us outline the chapter and then gives us alot of problems to do, forcing us to learn it by ourselves, so I wanted to thank you for posting this video!!

[profrobbob]

You are so welcome...and thank you for liking my video!

[JessFEZx]

thank you for all your  videos. Not only do I understand a lot more now, but you make it look fun too lol. You're the key to my success in pre-calc

[profrobbob]

Most learn FOIL as First Outer In Last as a pattern for learning to multiply two binomials and then get confused if they are multiplying expressions with three or more terms.

[georgesadler]

Professor RobBob, thank you for another superb video/lecture on Combining Functions with Operations. These are relatively simple operations that all students must know for future topics in math and science. The domain and range of these Combine Functions are also important especially when one function is divided by another.

[profrobbob]

As an example lets say f(x)=2x-1 and g(x)=x+2. Both of these functions have a domain of all real numbers...domain is the values you can plug into a function/relation. But if you set up f/g = (2x-1)/(x+2), this function has a division of 0 when x is -2, so the domain is all real numbers except -2. This is just one example, but when you check the domain of a combined function you must consider the parts that made that new function and the final simplified function.

[profrobbob]

You need to find common denominators. Multiply first by (1/5-x) top and bottom and then the second fraction by x top and bottom. Once you have common denominators add the numerators. You may want to check out my video Sum and Difference of Rational Expressions.

[profrobbob]

And THANK YOU for enjoying my teaching style and supporting by subscribing...I'm glad you found me too and I hope you will share my channel with your other classmates & friends:D

[profrobbob]

I do a little calligraphy here and there:) Thanks for the kind words and watching.

[profrobbob]

Well f(3) can't =3 because f(x) = x+2 and 3+2 is 5. But g(f(x)) = ln((x+2)^2)+2. Simplify that and then if extra information help you solve for x, just plug it in:)

[profrobbob]

You won't be able to get rid of the radical. You could rewrite g(x) as sqrt((x+3)^2) but you still won't be able to add them really. sqrt(2) + sqrt(3) does not equal sqrt(5)

[profrobbob]

And thank you for "liking" so many of my videos...keep watching and sharing, I appreciate your support:)