Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

=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.

Answer 5

pfft, STEP II

Answer 6

loser

Answer 7

I thought that Khan guy went to MIT at some point

Answer 8

brb

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

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.

Answer 13

Practice software? I haven't seen that.

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

it is really awesome

Answer 18

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,\[D= \mathbb{R}\]\[R= \mathbb{R}\]

Answer 19

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.
\[D=\mathbb{R}-\left\{ -1/3 \right\}\]\[R=\mathbb{R}-\left\{ -2/3 \right\}\]

Answer 20

Finished bmf

Answer 21

:) i wrote some stuff above

Answer 22

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

Answer 23

ok, will do that next time

Answer 24

I see the exercises.

Answer 25

It's pretty good.

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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.

Answer 31

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

Answer 32

So did you get any fans today?

Answer 33

no, but i dont care anyway

Answer 34

aw

Answer 35

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

Answer 36

Yeah, you said. When are the exams?

Answer 37

next tuesday

Answer 38

:)

Answer 39

You ready?

Answer 40

What do they test?

Answer 41

brb

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

you're in love with that site :)

Answer 46

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

Answer 47

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

Answer 48

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 :)

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

cool

Answer 54

just going to answer a question...

Answer 55

ok

Answer 56

btw, do you play computer games? =)

Answer 57

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

Answer 58

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

Answer 59

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 :(

Answer 60

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

Answer 61

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

Answer 62

University will require a lot of time ;)

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

thats what I will do

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

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

Answer 72

lol, maybe!

Answer 73

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

Answer 74

so, I am a bit strange in some areas

Answer 75

but I am slowly improving =)

Answer 76

you seem okay to me :-)

Answer 77

so, are you doing university?

Answer 78

finished

Answer 79

nice, what degree/subject?

Answer 80

advanced degree in pure mathematics and physics

Answer 81

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!

Answer 82

wow, i am impressed

Answer 83

ok, bye

Answer 84

bye:)