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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

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  1. anonymous
    • 5 years ago
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    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

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

  3. anonymous
    • 5 years ago
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    I saw you had some kind of debate with some guy called, I Newton or something...how did that pan out?

  4. anonymous
    • 5 years ago
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    =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.

  5. anonymous
    • 5 years ago
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    pfft, STEP II

  6. anonymous
    • 5 years ago
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    loser

  7. anonymous
    • 5 years ago
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    I thought that Khan guy went to MIT at some point

  8. anonymous
    • 5 years ago
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    brb

  9. anonymous
    • 5 years ago
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    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.

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

  11. anonymous
    • 5 years ago
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    Yeah, I've seen it. I send people to his site sometimes because the visuals are good, and the explanations are good enough.

  12. anonymous
    • 5 years ago
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    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.

  13. anonymous
    • 5 years ago
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    Practice software? I haven't seen that.

  14. anonymous
    • 5 years ago
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    PS I'm going to be answering this question...

  15. anonymous
    • 5 years ago
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    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

  16. anonymous
    • 5 years ago
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    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

  17. anonymous
    • 5 years ago
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    it is really awesome

  18. anonymous
    • 5 years ago
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    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,\[D= \mathbb{R}\]\[R= \mathbb{R}\]

  19. anonymous
    • 5 years ago
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    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. \[D=\mathbb{R}-\left\{ -1/3 \right\}\]\[R=\mathbb{R}-\left\{ -2/3 \right\}\]

  20. anonymous
    • 5 years ago
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    Finished bmf

  21. anonymous
    • 5 years ago
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    :) i wrote some stuff above

  22. anonymous
    • 5 years ago
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    bmf, if you want to talk, post a question or something to start a thread. paramore4lif3 is probably ticked ;)

  23. anonymous
    • 5 years ago
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    ok, will do that next time

  24. anonymous
    • 5 years ago
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    I see the exercises.

  25. anonymous
    • 5 years ago
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    It's pretty good.

  26. anonymous
    • 5 years ago
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    But what if I want to train people for STEP? lol

  27. anonymous
    • 5 years ago
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    do you like the mind map with all the topics interconected? (used google maps LOL)

  28. anonymous
    • 5 years ago
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    I think it's good enough for most school kids.

  29. anonymous
    • 5 years ago
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    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

  30. anonymous
    • 5 years ago
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    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.

  31. anonymous
    • 5 years ago
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    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

  32. anonymous
    • 5 years ago
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    So did you get any fans today?

  33. anonymous
    • 5 years ago
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    no, but i dont care anyway

  34. anonymous
    • 5 years ago
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    aw

  35. anonymous
    • 5 years ago
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    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

  36. anonymous
    • 5 years ago
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    Yeah, you said. When are the exams?

  37. anonymous
    • 5 years ago
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    next tuesday

  38. anonymous
    • 5 years ago
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    :)

  39. anonymous
    • 5 years ago
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    You ready?

  40. anonymous
    • 5 years ago
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    What do they test?

  41. anonymous
    • 5 years ago
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    brb

  42. anonymous
    • 5 years ago
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    well, I am almost ready :) everything from high school, it shouldn't be that hard, maybe some derivation, functions, and stuff like that

  43. anonymous
    • 5 years ago
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    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

  44. anonymous
    • 5 years ago
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    and today is actually a bad day, yesterday i noticed that there was about 32000 lesson views

  45. anonymous
    • 5 years ago
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    you're in love with that site :)

  46. anonymous
    • 5 years ago
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    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

  47. anonymous
    • 5 years ago
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    Yeah it's good. What's the course you want to do at university?

  48. anonymous
    • 5 years ago
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    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 :)

  49. anonymous
    • 5 years ago
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    Oh, that's right. Did you drop out of university or something?

  50. anonymous
    • 5 years ago
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    Hope I didn't say anything to tick you off.

  51. anonymous
    • 5 years ago
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    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

  52. anonymous
    • 5 years ago
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    and I usually dont get ticked off =D even if ppl say really bad stuff :)

  53. anonymous
    • 5 years ago
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    cool

  54. anonymous
    • 5 years ago
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    just going to answer a question...

  55. anonymous
    • 5 years ago
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    ok

  56. anonymous
    • 5 years ago
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    btw, do you play computer games? =)

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

  58. anonymous
    • 5 years ago
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    No, I don't really play computer games :(

  59. anonymous
    • 5 years ago
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    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 :(

  60. anonymous
    • 5 years ago
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    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

  61. anonymous
    • 5 years ago
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    I might quit for good, if university will actually require a lot of time...

  62. anonymous
    • 5 years ago
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    University will require a lot of time ;)

  63. anonymous
    • 5 years ago
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    then I am quiting, but it is very hard... I wish I never started

  64. anonymous
    • 5 years ago
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    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

  65. anonymous
    • 5 years ago
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    I wish MMORPGs were never created... they suck too much precious time

  66. anonymous
    • 5 years ago
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    Yeah, you should lay off them...and study/exercise.

  67. anonymous
    • 5 years ago
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    thats what I will do

  68. anonymous
    • 5 years ago
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    Good...you're a funny person ;)

  69. anonymous
    • 5 years ago
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    :) because??? feel free to tell me =D

  70. anonymous
    • 5 years ago
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    I don't know. It's just an impression.

  71. anonymous
    • 5 years ago
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    well, maybe I spend too much time indoors infront of my PC

  72. anonymous
    • 5 years ago
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    lol, maybe!

  73. anonymous
    • 5 years ago
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    I have been quite antisocial all my life, unfortunatelly :(

  74. anonymous
    • 5 years ago
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    so, I am a bit strange in some areas

  75. anonymous
    • 5 years ago
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    but I am slowly improving =)

  76. anonymous
    • 5 years ago
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    you seem okay to me :-)

  77. anonymous
    • 5 years ago
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    so, are you doing university?

  78. anonymous
    • 5 years ago
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    finished

  79. anonymous
    • 5 years ago
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    nice, what degree/subject?

  80. anonymous
    • 5 years ago
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    advanced degree in pure mathematics and physics

  81. anonymous
    • 5 years ago
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    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!

  82. anonymous
    • 5 years ago
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    wow, i am impressed

  83. anonymous
    • 5 years ago
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    ok, bye

  84. anonymous
    • 5 years ago
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    bye:)

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