Composition of Functions
ฝัง
- เผยแพร่เมื่อ 26 ส.ค. 2024
- I introduce composition of functions and discuss domain.
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My AS level math exam is less than 24 hours away, and I was panicking over functions till now.
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When setting up the domain of a composite function, check the domain of the inside function first...in my example that was G(x). Then after you have set up and simplified your composition f(g(x)) check for domain again.
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No...(FoG)(x) is equivalent to F(G(x)) and you are substituting G into F where (F+G)(x) is you adding the two functions....or Combining Functions if you want to watch that video. Thank you very much for watching again:)
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Professor RobBob ,thank you for an outstanding video/lecture on the Composition of Functions in classic Algebra Two/ Precalculus /College Algebra.
Best tutorial video I have come across on TH-cam... thank you so much :)
My teacher plays u all the time. I love your entrance. Starts the lesson right. U made me love math for the first time.
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I have a huge math final this week and I just stumbled across this video and it helped me tremendously. I understand functions now! thanks so much!
OMG i finally got a 100% on my test. Thank you sir!!! Wish u were my teacher
You can either multiply together (3x+5)(2+x)^2 and then plug in -2 or plug -2 into each function sperately, get a numerical answer, and then multiply those numbers together which is less work.
thank you for helping me learn and prep for my test by relearning it
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Thank you so much for making this so much easier than what it really looks !!!!
This really helped me, I have been lost and got the concept with your usage of parenthesis to fill in functions...
THANK YOU! Best Video to explain how to find the domain!!
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Oh, wow! Did I just understand this lesson???? I've been struggling with this concept. Won't blame my teacher, it's just me having a hard time. Since I finally understood all the steps, now I'll just watch it a few more times, until I can replicate it myself. I have a test next week, so PADIUSH (thank you in Nahuat Pipil) !!!
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Very helpful video, I'm retaking pre-calc in college, and my professor just made this concept I used to know so confusing, I had to clarify
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Easy To Understand and of course it's fun to learn.Will wait for more videos about composite functions and it'll help if you could do composite relation about matrix.Thank You
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Just a friendly observation regarding the domain . At about 8:30 you ask "can x be -1?" I believe we should be looking for an x-value that would make g(x)=-1, since this output will be used as an input by f(x). Therefore , the x-value which makes g(x)=-1 is actually x=-3, which you had already excluded.
That is a very good suggestion and thank you for watching:)
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hello sir this is varun all the way from india. great lecture sir.
helped me a lot
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You're such a amazing teacher! Can you answer this question, please?
Determine whether the statements are True or False. Justify your answer with an explanation.
If you are given two functions f(x) and g(x), you can calculate (f ○g)(x) if and only if the range of g is a subset of the domain of f.
I don't know if its too late to answer or not but I hope it helps to anyone who sees it!
The statement you said is definitely true.
There are two functions f(x) and g(x).
(f ○g)(x) means f(g(x)) which means you are putting a value of function g(x) inside the function f(x). The value you are putting inside f(x) is the value you got when you put x inside the function g(x). And those values you get by putting values in a function are called the Range of that function.
Now if you put the values or Range of g(x) inside the function f(x) that gets the value undefined like if you put value 2 inside g(x) and it gave you 0 and then you put that value 0 inside f(x) and the output gets undefined then you can't put that value. Meaning you can put only those values of g(x) inside f(x) for which your output gets defined.
And the values you can put inside a function is called Domain of that function.
Again, to clarify that Domain is the set of values that you can put inside a function so that your output gets defined and the set of values you get after putting the value in function is called Range of that function.
MEANING, that you can only put the values from the range of the function g(x) for which the the function gets defined meaning that the range of values from g(x) must also be domain of f(x). And is some set of values is under another set of values then the set is called a subset meaning a subdivision of that set.
So, your statement 'If you are given two functions f(x) and g(x), you can calculate (f ○g)(x) if and only if the range of g is a subset of the domain of f.' is completely true.
I hope it helps!
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Can you let me know where in the video you are talking about? The only part I can guess is where I added fractions and there was a common denominator...you don't add common denominators or where I was dividing and the x's divided each other out.
i'll i had to watch was the first 20 seconds and I figured it out.
You just saved my life pro Rob
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You look like a math geek. Out of all of the videos, I know I can trust yours. You also explain things alot better. WHy couldn't you be my math teacher?
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I'm in sophomore year in one of the toughest schools in our country, and this video still did better in making me understand the subject than my own professor. Thanks Prof RobBob!
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@EsperTinaVI THAT'S what must be wrong with me! I grew up in schools with chalk boards and have used them for the 17 years I have been teaching. I always thought I must be a little crazy to love my job so much...it is chalk poisoning. haha. I will have to look into the health thing...my memory says it was an allergy thing...and maybe all the dust getting into these new fangled electronic things.
Thanks for the video. I am currently a junior in HS and I want to do engineering but I am a little behind on math. I have algebra 1 and 2 and geometry finished. My algebra skills I know I still need to work on. What does composition of functions exactly benefit you for in pre calc and calculus? And what stuff in calculus is used the most from algebra?
Is there a charge for students to use the website?
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great video, thank you for doing this. I passed it on
You are very good teacher I loved you you very helped me thank you
This is Very Helpful than Khan Academy,straight to the point no whatsoever.