Penny Arcade Forums› Help / Advice Forum
The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.

Pre-Calc Question

milehighmilehigh Registered User regular
edited January 2009 in Help / Advice Forum
I may be over thinking this, but the following problem is giving me a headache, I'm not trying to get anyone to do this for me, but hints in the right direction would be greatly appreciated....Maybe I'm overlooking some simple law/rule that will make this easy...

"Find a function such that f(a+b) = f(a)f(b) Why does your function satisfy this condition?"

I've toyed around with a variety of functions and methods and can't seem to get anything that will cause these to equal each other. Thanks in advance for any help.

milehigh on

Posts

  • enlightenedbumenlightenedbum Registered User regular
    edited January 2009
    There are two, they're both very very simple. I dunno about a good hint, but think about functions and are they distributive or associative or any of that stuff?

    enlightenedbum on
    The idea that your vote is a moral statement about you or who you vote for is some backwards ass libertarian nonsense. Your vote is about society. Vote to protect the vulnerable.
  • LewishamLewisham Registered User regular
    edited January 2009
    Spoiler'd so as not to ruin it.
    f(x) = x * 0

    f(x) = x/x

    That's my guess anyway.

    Lewisham on
  • PaleCommanderPaleCommander Registered User regular
    edited January 2009
    Unfortunately, this question isn't terribly "hintable" (just giving you the answer wouldn't help you on a future test or such). Try to think of rules you may know for breaking up a sum. For example, the distributive property says that 2 * (3 + 5) = 2 * 3 + 2*5. That's not what you're looking for, since that turns into addition instead of multiplication.

    Do you know any other similar rules for other operations?

    PaleCommander on
    steam_sig.png
  • enlightenedbumenlightenedbum Registered User regular
    edited January 2009
    Lewisham wrote: »

    That's my guess anyway.

    Second one of those functions isn't defined at 0.

    enlightenedbum on
    The idea that your vote is a moral statement about you or who you vote for is some backwards ass libertarian nonsense. Your vote is about society. Vote to protect the vulnerable.
  • LewishamLewisham Registered User regular
    edited January 2009
    enlightenedbum wrote: »
    Lewisham wrote: »

    That's my guess anyway.

    Second one of those functions isn't defined at 0.

    Rats :x
    try:
   second function
catch: DivideByZeroError
   print "You were bloody told this would happen Lewis, now see the mess you're in"

    Lewisham on
  • PaleCommanderPaleCommander Registered User regular
    edited January 2009
    Lewisham wrote: »
    Spoiler'd so as not to ruin it.
    f(x) = x * 0

    f(x) = x/x

    That's my guess anyway.

    You're doing quite a good job of finding the pathological (by which I mean fun) examples. I suspect the person who wrote the problem has a specific type of answer in mind (namely, a non-constant function) which requires more math but isn't as cool.

    Edit: you too, Virum.

    PaleCommander on
    steam_sig.png
  • VirumVirum Registered User regular
    edited January 2009
    What can you do to make the function always return 1?
    x^0

    Virum on
    http://www.joshuanitschke.com
  • enlightenedbumenlightenedbum Registered User regular
    edited January 2009
    PaleCommander wrote: »
    Lewisham wrote: »
    Spoiler'd so as not to ruin it.
    f(x) = x * 0

    f(x) = x/x

    That's my guess anyway.

    You're doing quite a good job of finding the pathological (by which I mean fun) examples. I suspect the person who wrote the problem has a specific type of answer in mind which requires more math but isn't as cool.

    Edit: you too, Virum.

    The complicated answers make me think of group theory and I don't want to think about that, so I say aim him towards the fun ones.

    enlightenedbum on
    The idea that your vote is a moral statement about you or who you vote for is some backwards ass libertarian nonsense. Your vote is about society. Vote to protect the vulnerable.
  • LewishamLewisham Registered User regular
    edited January 2009
    PaleCommander wrote: »

    You're doing quite a good job of finding the pathological (by which I mean fun) examples. I suspect the person who wrote the problem has a specific type of answer in mind which requires more math but isn't as cool.

    Edit: you too, Virum.

    Well now I'm all excited.

    One thing about maths is I find the idea of it usually pretty cool, I just suffer at the execution.

    That's why I'm trying out data mining programs. All the fun, none of the programming of equations :)

    I'm looking forward to what this thread ends up with!

    Lewisham on
  • Folken FanelFolken Fanel anime af When's KoFRegistered User regular
    edited January 2009
    f(x) = 1

    Folken Fanel on
    Twitter: Folken_fgc Steam: folken_ XBL: flashg03 PSN: folken_PA SFV: folken_
    Dyvim Tvar wrote: »
    Characters I hate:

    Everybody @Folken Fanel plays as.
  • enlightenedbumenlightenedbum Registered User regular
    edited January 2009
    Folken Fanel wrote: »
    An answer

    Shush, he didn't want an answer.

    enlightenedbum on
    The idea that your vote is a moral statement about you or who you vote for is some backwards ass libertarian nonsense. Your vote is about society. Vote to protect the vulnerable.
  • PaleCommanderPaleCommander Registered User regular
    edited January 2009
    enlightenedbum wrote: »
    PaleCommander wrote: »
    Lewisham wrote: »
    Spoiler'd so as not to ruin it.
    f(x) = x * 0

    f(x) = x/x

    That's my guess anyway.

    You're doing quite a good job of finding the pathological (by which I mean fun) examples. I suspect the person who wrote the problem has a specific type of answer in mind which requires more math but isn't as cool.

    Edit: you too, Virum.

    The complicated answers make me think of group theory and I don't want to think about that, so I say aim him towards the fun ones.

    In this case, group theory is ridiculous overkill. So's calculus, complex analysis, and anything else that's beyond pre-calc. Sheesh.

    PaleCommander on
    steam_sig.png
  • enlightenedbumenlightenedbum Registered User regular
    edited January 2009
    PaleCommander wrote: »
    enlightenedbum wrote: »
    PaleCommander wrote: »
    Lewisham wrote: »
    Spoiler'd so as not to ruin it.
    f(x) = x * 0

    f(x) = x/x

    That's my guess anyway.

    You're doing quite a good job of finding the pathological (by which I mean fun) examples. I suspect the person who wrote the problem has a specific type of answer in mind which requires more math but isn't as cool.

    Edit: you too, Virum.

    The complicated answers make me think of group theory and I don't want to think about that, so I say aim him towards the fun ones.

    In this case, group theory is ridiculous overkill. So's calculus, complex analysis, and anything else that's beyond pre-calc. Sheesh.

    I've been restudying for the GRE math lately. Group theory comes up a lot.

    enlightenedbum on
    The idea that your vote is a moral statement about you or who you vote for is some backwards ass libertarian nonsense. Your vote is about society. Vote to protect the vulnerable.
  • milehighmilehigh Registered User regular
    edited January 2009
    Ok, so I just came to the conclusion that this would also work: f(x)=e^x.

    This would result in the first side (a+b) equaling e^(a+b) and the second side being (e^a)(e^b) which by the rules of exponents should be equal.

    Am I thinking about this correctly? All the help is appreciated.

    milehigh on
  • PaleCommanderPaleCommander Registered User regular
    edited January 2009
    Bingo!

    PaleCommander on
    steam_sig.png
  • enlightenedbumenlightenedbum Registered User regular
    edited January 2009
    I like f(x) = 0 and f(x) = 1 far more though.

    enlightenedbum on
    The idea that your vote is a moral statement about you or who you vote for is some backwards ass libertarian nonsense. Your vote is about society. Vote to protect the vulnerable.
  • SmasherSmasher Starting to get dizzy Registered User regular
    edited January 2009
    You're looking for a function where adding a small value to the input results in a multiplicative increase in the output. Also, f(a+0) = f(a)f(0) which means f(0) = 1. What class of functions fits those criteria?

    Edit: Guess I should have refreshed before posting. In any case it should work for any base (other than 0), not just e.

    Smasher on
  • Folken FanelFolken Fanel anime af When's KoFRegistered User regular
    edited January 2009
    enlightenedbum wrote: »
    I like f(x) = 0 and f(x) = 1 far more though.

    e^x is much more elegant and nontrivial though.

    Folken Fanel on
    Twitter: Folken_fgc Steam: folken_ XBL: flashg03 PSN: folken_PA SFV: folken_
    Dyvim Tvar wrote: »
    Characters I hate:

    Everybody @Folken Fanel plays as.
Sign In or Register to comment.
Penny Arcade Forums› Help / Advice Forum