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anonymous
 5 years ago
I have to determine the domain and range of the f(g(x)) and g(f(x))
f(x)=1/x+3 and g(x)=2/x
anonymous
 5 years ago
I have to determine the domain and range of the f(g(x)) and g(f(x)) f(x)=1/x+3 and g(x)=2/x

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey lokisan, do you know what is the rank after HERO called? I know there are a few more ranks, but I have no idea what are they called, so any idea? have you ever seen anyone on openstudy ever with a higher rank than hero? just asking SORRY papamore for posting this here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hi BMF  have no idea. I guess we'd find out sooner if people who get help actually clicked the link!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I saw you had some kind of debate with some guy called, I Newton or something...how did that pan out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0=D that was interesting =D he was basically saying that he is smarter than anyone here because he can do STEP II problems and stuff like that., And he was sayin that Khan Academy founder is a "average intelligent jerk". I told him that that "avg intell jerk" got 2 million dollar google award and microsoft award and has helped more than a million students in the world study maths, but that did not change his mind.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I thought that Khan guy went to MIT at some point

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I dont know about MIT but I am sure that he has 5 degrees and also worked at a hedge fund or something, but then the point that he made an online training resourse that is 100% free and has helped millions is enough for me. I mean, I learned stuff in 1 hour that usualy takes weeks to learn in school. It is great for me, especially some physics and finances stuff.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0he has a nice video now in the front page of the http://www.khanacademy.org features Bill Gates at the end =D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, I've seen it. I send people to his site sometimes because the visuals are good, and the explanations are good enough.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, I am not saying the teaching resource is the best, but hey, it does the work and it does it for free for anyone who is willing to learn. Also, the practice software is just GREAT for highschool kids from grade 1 all the way to grade 12.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Practice software? I haven't seen that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0PS I'm going to be answering this question...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0really? it is like the main point of the site, you keep completing questions until you are stuck, then you watch a vid, and try again, and once you are good at a topic, you move on to the next one

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just go to the website and click on PRACTICE button, you will be taken to a mind map of maths topics from addition all the way up to derivation and so on. click on any of those and see how it works, also, try the "I'd like a hint" button, to see how the software solves problems step by step

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0paramore4lif3, you're asked to consider the domain and range of composite functions. For the first one, f(g(x)), you have,\[f(g(x))=\frac{1}{g(x)}+3=\frac{1}{(2/x)}+3=\frac{x}{2}+3\]This is the equation of a straight line. It can take all real values of x, and its image (range) is also, all real x. So the domain and range of f(g(x)) is,\[D= \mathbb{R}\]\[R= \mathbb{R}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For the second composition, you have g(f(x)):\[g(f(x))=\frac{2}{\frac{1}{x}+3}=\frac{2x}{1+3x}\]This function can take all real values of x, except for x=1/3, for here, the denominator is 0 and the function is undefined. To find the range, we can use the fact that the domain of the inverse function of g(f(x)) is equal to the range of g(f(x)). Call the composite above, h(x). By the definition of the inverse function,\[h(h^{1}(x))=\frac{2h^{1}(x)}{1+3h^{1}(x)}=x \rightarrow h^{1}(x)=\frac{x}{3x+2}\]The domain of the inverse function here is all of x real, except for x=2/3, for here, the denominator is zero. From what was said above, the domain of the inverse is equal to the range of the original (i.e. the range of h(x) = g(f(x))), and so the range of g(f(x)) is all x real except for x=2/3. \[D=\mathbb{R}\left\{ 1/3 \right\}\]\[R=\mathbb{R}\left\{ 2/3 \right\}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0:) i wrote some stuff above

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0bmf, if you want to talk, post a question or something to start a thread. paramore4lif3 is probably ticked ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, will do that next time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But what if I want to train people for STEP? lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you like the mind map with all the topics interconected? (used google maps LOL)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think it's good enough for most school kids.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well, it is not ready for STEP yet, because its main target is high school topics, for the majority, the multitudes. the most difficult stuff that you can currently find there is http://www.khanacademy.org/#Calculus and http://www.khanacademy.org/#Differential%20Equations

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't find anything wrong with his stuff. He doesn't do things the way I would sometimes, but who cares? Like you said, people can watch and get a handle on things in a couple of minutes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, thats the thing, a dedicated grade 8 student could learn almost everything he will need in grades 9 to 12 in like a month

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So did you get any fans today?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, but i dont care anyway

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i dont even spend much time here, and dont help often, so it is almost imposible for me to get fans. =D but then I am studying myself, for entrance examinations to a university. And it DAMN hard to get in, only one out of every ten applicants get in

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, you said. When are the exams?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well, I am almost ready :) everything from high school, it shouldn't be that hard, maybe some derivation, functions, and stuff like that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw, i just noticed on the khan academy visitors counter that today, since midnight, 9872 people have watched a video lesson =D. Imagine that, like 10000 people learning something good in one day. not bad

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and today is actually a bad day, yesterday i noticed that there was about 32000 lesson views

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you're in love with that site :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not realy, unfortunately it only covers things up to a rather basic level, so I will not be able to use it for long..... but, IT IS GREAT. I will advertise this site to every one. I know so many kids who would benefit from this. And the game like point and trophy/award systems is quite addictive, kids actually start to solve maths instead of games LOL

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah it's good. What's the course you want to do at university?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0at first I wanted to do electronics, and later computer science, but then, on the last week before application, I changed my mind and signed up for Media Engineering :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, that's right. Did you drop out of university or something?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hope I didn't say anything to tick you off.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no LOL, i just wrote that for fun =D sometimes i just say some weird stuff for fun :) oh, and my internet was stuck just now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and I usually dont get ticked off =D even if ppl say really bad stuff :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just going to answer a question...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw, do you play computer games? =)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I guess not, because you would be playing right now =D some of those MMORPGs are VERY addictive... I wish I had time...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, I don't really play computer games :(

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you must have a strong will then, because I love MMORPGs like EVE Online so much I could not stop even if I wanted to :( it is actually sad,  addiction to MMORPGs :(

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the only reason I dont play it now is because I have exams soon, so I have to study and keep my mine clear for some time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I might quit for good, if university will actually require a lot of time...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0University will require a lot of time ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then I am quiting, but it is very hard... I wish I never started

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0EVE Online has like 300 000 players in ONE universe.... it is pretty cool and addictive.... sometimes I feel like just playing all the day

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I wish MMORPGs were never created... they suck too much precious time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, you should lay off them...and study/exercise.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good...you're a funny person ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0:) because??? feel free to tell me =D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't know. It's just an impression.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well, maybe I spend too much time indoors infront of my PC

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have been quite antisocial all my life, unfortunatelly :(

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, I am a bit strange in some areas

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but I am slowly improving =)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you seem okay to me :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, are you doing university?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nice, what degree/subject?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0advanced degree in pure mathematics and physics

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0anyways, I'm exhausted. It's after 2am and I have a lot of traveling to do tomorrow :( Have to go to bed. Study hard and stay off the games!
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