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

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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- katieb

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- anonymous

hey 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

Hi BMF - have no idea. I guess we'd find out sooner if people who get help actually clicked the link!

- anonymous

I saw you had some kind of debate with some guy called, I Newton or something...how did that pan out?

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- anonymous

=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

pfft, STEP II

- anonymous

loser

- anonymous

I thought that Khan guy went to MIT at some point

- anonymous

brb

- anonymous

I 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

he has a nice video now in the front page of the http://www.khanacademy.org
features Bill Gates at the end =D

- anonymous

Yeah, I've seen it. I send people to his site sometimes because the visuals are good, and the explanations are good enough.

- anonymous

yeah, 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

Practice software? I haven't seen that.

- anonymous

PS I'm going to be answering this question...

- anonymous

really? 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

just 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

it is really awesome

- anonymous

paramore4lif3, 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

For 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

Finished bmf

- anonymous

:) i wrote some stuff above

- anonymous

bmf, if you want to talk, post a question or something to start a thread. paramore4lif3 is probably ticked ;)

- anonymous

ok, will do that next time

- anonymous

I see the exercises.

- anonymous

It's pretty good.

- anonymous

But what if I want to train people for STEP? lol

- anonymous

do you like the mind map with all the topics interconected? (used google maps LOL)

- anonymous

I think it's good enough for most school kids.

- anonymous

well, 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

I 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

yeah, 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

So did you get any fans today?

- anonymous

no, but i dont care anyway

- anonymous

aw

- anonymous

i 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

Yeah, you said. When are the exams?

- anonymous

next tuesday

- anonymous

:)

- anonymous

You ready?

- anonymous

What do they test?

- anonymous

brb

- anonymous

well, I am almost ready :) everything from high school, it shouldn't be that hard, maybe some derivation, functions, and stuff like that

- anonymous

btw, 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

and today is actually a bad day, yesterday i noticed that there was about 32000 lesson views

- anonymous

you're in love with that site :)

- anonymous

not 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

Yeah it's good. What's the course you want to do at university?

- anonymous

at 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

Oh, that's right. Did you drop out of university or something?

- anonymous

Hope I didn't say anything to tick you off.

- anonymous

no 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

and I usually dont get ticked off =D even if ppl say really bad stuff :)

- anonymous

cool

- anonymous

just going to answer a question...

- anonymous

ok

- anonymous

btw, do you play computer games? =)

- anonymous

I guess not, because you would be playing right now =D some of those MMORPGs are VERY addictive... I wish I had time...

- anonymous

No, I don't really play computer games :(

- anonymous

you 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

the 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

I might quit for good, if university will actually require a lot of time...

- anonymous

University will require a lot of time ;)

- anonymous

then I am quiting, but it is very hard... I wish I never started

- anonymous

EVE 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

I wish MMORPGs were never created... they suck too much precious time

- anonymous

Yeah, you should lay off them...and study/exercise.

- anonymous

thats what I will do

- anonymous

Good...you're a funny person ;)

- anonymous

:) because??? feel free to tell me =D

- anonymous

I don't know. It's just an impression.

- anonymous

well, maybe I spend too much time indoors infront of my PC

- anonymous

lol, maybe!

- anonymous

I have been quite antisocial all my life, unfortunatelly :(

- anonymous

so, I am a bit strange in some areas

- anonymous

but I am slowly improving =)

- anonymous

you seem okay to me :-)

- anonymous

so, are you doing university?

- anonymous

finished

- anonymous

nice, what degree/subject?

- anonymous

advanced degree in pure mathematics and physics

- anonymous

anyways, 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!

- anonymous

wow, i am impressed

- anonymous

ok, bye

- anonymous

bye:)

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