Functional Equations... Sorta

by MP8148, Apr 29, 2019, 9:43 PM

Source: 2015 HMMT November Guts #26

Let $f: \mathbb{R}^{+} \to \mathbb{R}$ be a continuous function satisfying $f(xy) = f(x) + f(y) + 1$ for all positive reals $x, y$ . If $f(2) = 0$ , compute $f(2015)$ .

Thought Process

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Wow nice thought process! For me what gave the logarithm part away (after noticing it looks like log addition) is $\mathbb{R}^+$ . The fact that the imput has to be a positive real and the output is any real kinda gives the logarithm part away.

by montresor, Jun 25, 2019, 8:43 AM

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rip jun-dec post
by mathisawesome2169, Jan 15, 2023, 5:22 AM
rip may post
by MP8148, Jun 1, 2022, 5:27 AM
The question is, how will it end?
and the smart answer is "I won't be alive to see it end so I won't care and I will just get this midterm done"
by RedFlame2112, Feb 15, 2022, 11:57 PM
well the universe will end anyways
by kevinmathz, Feb 8, 2022, 2:44 PM
@below this is why you shouldn't waste your time thinking about life, because it doesn't give happy results
by MP8148, Jan 28, 2022, 3:51 AM
why is life so short
by MP8148, Jan 26, 2022, 11:25 PM
https://www.urbandictionary.com/define.php?term=anti-simp

lol what

didn't know this is an actual word
by MP8148, Nov 28, 2021, 4:01 PM
you should antisimp for college board tbh
by mathisawesome2169, Nov 28, 2021, 2:31 PM
good idea
by v4913, Nov 27, 2021, 10:48 PM
tired of simping for college board
by MP8148, Nov 2, 2021, 8:11 PM
waitttttttt why default avatar (
by MrOreoJuice, Nov 2, 2021, 2:04 PM
is it just me or did the total number of blogposts mysteriously decrease by 1? I'm pretty sure it went from 178 to 177
by MP8148, Oct 29, 2021, 12:18 PM
woops i should have mentioned, it was the problem with which the bary cs pdf was attached (linked in the recent geo marathon) and also thanks for the asy guide link
by MrOreoJuice, Sep 27, 2021, 8:03 AM
idk which diagram you're referring to, but thx. it takes practice to get better at asy (like everything else lol), but i think this is pretty good
by MP8148, Sep 26, 2021, 10:11 PM
omgg that diagram is so hawt
you should make an asy tutorial lol
by MrOreoJuice, Sep 26, 2021, 6:12 PM
*shouts not shorts
by MP8148, Dec 4, 2019, 5:42 AM
Wow asymptote works in shorts that’s epic :O
by MP8148, Dec 4, 2019, 5:42 AM
$[asy] unitsize(1cm); pair A = dir(110), B = dir(210), C = dir(330); draw(A--B--C--A); [/asy]$
by MP8148, Dec 4, 2019, 5:40 AM
Pen advantages: Easier to write with (IMO, esp. if you have a decent pen that costs more than 25 cents), nicer to look at.
Pencil advantages: Erasable.

I tried erasable pens but they just feel like darker pencils.
by Frestho, Aug 31, 2019, 6:35 PM
I use pens for everything, except at real [math] contests where I use pencils. Weird right
by MP8148, Aug 22, 2019, 5:58 AM
Lol when I mock AMCs and AIMEs I use my pen.
by Frestho, Aug 22, 2019, 4:43 AM
Sure.
by MP8148, Aug 18, 2019, 5:30 PM
Contrib pls?
by kevinmathz, Aug 6, 2019, 10:07 AM
$\text{[math]}$
by Frestho, Jun 5, 2019, 1:34 AM
Apparently it does.
by MP8148, May 29, 2019, 2:50 AM
Just curious: does LaTeX work in shoutboxes? $\dfrac{2}{3}$
by MP8148, May 29, 2019, 2:47 AM
Nice blog name
by Frestho, Mar 11, 2019, 5:11 PM
I'll definitely make much more. 1 per month is the lower bound .
by MP8148, Dec 19, 2018, 5:08 AM
Only one per month?! You should make it more
by hashtagmath, Dec 18, 2018, 5:22 AM

107 shouts

Prove AB, AC, AD are concurrent

Functional Equations... Sorta

by MP8148, Apr 29, 2019, 9:43 PM

1 Comment