In the Old Republic, where do little Jedi come from?
If mastery of the Force is hereditary, how are the Jedi so numerous?
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t Let  $f(xy) =f(x)f(y)$ for all $x,y\geq 0$. Show that $f(x) = x^p$ for some $p$.    I am not very experienced with proof. If we let $g(x)=\log (f(x))$ then this is the same as  $g(xy) = g(x) + g(y)$   I looked up the hint and it says let $g(x) = \log f(a^x) $   The wikipedia page for functional equations only states the form of the solutions without proof.  Attempt  Using the hint (which was like pulling a rabbit out of the hat)  Restricting the codomain $f:(0,+\infty)\rightarrow (0,+\infty)$ so that we can define the real function $g(x) =  \log f(a^x)$ and we have $$g(x+y) = g(x)+ g(y)$$   i.e $g(x) = xg(1)$ as $g(x)$ is continuous (assuming $f$ is).  Letting $\log_a f(a) = p$ we get $f(a^x) =a^p $. I do not have a rigorous argument but I think I can conclude that $f(x) = x^p$ (please fill any holes or unspecified assumptions) Different solutions are invited Flagging accepted "answers" How Do You Use An Image As The World Background? Taking a skyline photo with a person closer to the camera during night time How can I take a photo which shows the skyline and the person who is standing around six feet away from the camera with proper lighting at night?   For taking just the skyline I've used long shutter speed and it turned out great, but when including a person on it, the person becomes  blurry because it's impossible for a person to remain static for that long.   Ps.  I do have two flashes, 35mm prime lens as well as 18-300mm zoom lenses as well. The camera I use is Nikon D7200. How to upload string as file with jQuery or other js framework What is the best way to clean lenses and filters? After removing dust with an air pomp and a brush, what are you using to remove stains from the lens and filters?  So far I'm using the liquid from a Giotto's CL 1002 cleaning kit for the lens, but I'm not sure what should I use for the filters, and if there is some better alternative.  Also, what kind of brushes are recommended? I recently installed Ubuntu 14.04, then I installed lamp-server and placed my webpages in /var/www directory, but when I opened localhost in the browser there was nothing. I think that happened because Zend updated Apache.  Whatever the reason may be, I want to know where to keep my php files so that I can access them from my browser. I have been given the task to rewrite a function as a sum of an even and an odd function. But when I went to analyze the parts of the original function I noticed that one part was neither even nor odd.   The original function was: $g(x) = (x + 1) / (x^2 - 3x + 4$)  After analyzing I realized that when using f(-x) to determine symmetry it produced a 'neither' result. How would I go about writing a function that is neither even nor odd as an even function. (It would have to be an even function as the (x+1) part of the original function is odd and since I need to write it as a sum of even and odd, the denominator would need to be even. The package babel with the ngerman option (and most other languages as well, but not english) provides the shorthand "|, which prevents a ligature at the given position (see p. 81 of the , e.g. Auf"|lage will result in the word Auflage without an fl-ligature (as is desired because, in German, you don't want ligatures across morpheme borders).  However, when placed in a macro, "| doesn't work anymore. Why is this and how can I circumvent it?  \documentclass{article}  %\usepackage[T1]{fontenc}% doesn't help \usepackage[ngerman]{babel}  \newcommand{\foo}{"|}  \begin{document}  ff  f"|f  f\foo f  \end{document} Unicode char {U+200B} When I try to cite more than two authors, I got this: ! Package inputenc Error: Unicode char ​ (U+200B) (inputenc)                not set up for use with LaTeX.   \documentclass[a4paper,oneside,BCOR=10mm,12pt,titlepage]{scrreprt}  \usepackage[polutonikogreek,ngerman,english]{babel} \usepackage[maxlevel=4,autostyle,german=guillemets]{csquotes} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[style=mla]{biblatex} \DeclareMultiCiteCommand{\parencites}[\mkbibparens]{\parencite}{\multicitedelim‌​}  \begin{document}  \parencites[cf.][]{key1}{key2}{key3}  \end{document} JavaScript YAML Parser Is "I am sat" bad English? I believe it is incorrect and instead either the present continuous     I am sitting   or the predicate adjective     I am seated   should be used.  I hear this quite often, however, and ultimately usage overrules formality.  Does anybody know where this originated or how to describe it grammatically? Editing text file with Vim does not update tail -f uniq command not working properly? So I'm checking the md5 hash of my files with this as my output:  657cf4512a77bf47c39a0482be8e41e0  ./dupes2.txt 657cf4512a77bf47c39a0482be8e41e0  ./dupes.txt 8d60a927ce0f411ec94ac26a4785f749  ./derpina.txt 15f63928b8a1d5337137c38b5d66eed3  ./foo.txt 8d60a927ce0f411ec94ac26a4785f749  ./derp.txt   However, after running find . -type f -exec md5sum '{}' ';' | uniq -w 33 to find the unique hashes I get this:  657cf4512a77bf47c39a0482be8e41e0  ./dupes2.txt 8d60a927ce0f411ec94ac26a4785f749  ./derpina.txt 15f63928b8a1d5337137c38b5d66eed3  ./foo.txt 8d60a927ce0f411ec94ac26a4785f749  ./derp.txt   From my understanding, only one of either derpina.txt or derp.txt should be showing up since their hashes are the same. Am I missing something? Can anyone enlighten me as to why it outputs like this? Replace \input{fileX} by the content of fileX automatically How can I perform a t-test (or another hypothesis test) on NPS (Net Promoter Score) results? Here is an explanation of how NPS is calculated:    I'm interested in testing two net promoter scores to determine if they are statistically different. I read a great answer to calculating margin of error for NPS (see link below), but I'm really interested in testing to see if there is a difference between two scores, because I suspect that our results aren't as "different" from year to year as they appear to be.    Is this at all possible? I understand t-tests are typically used to test whether two different record sets are statistically different. But is it possible to test Net Promoter Scores, either with a t-test or some other hypothesis test?  Any ideas you have would be a great help. Thank you! Audio is working, but the speaker test doesn't work I've installed Ubuntu 12.04 LTS from a minimal cd on a netbook (Asus 1001 PXD). I've installed the ubuntu-desktop package using the --no-install-recommends option.  Everything works fine, except the "sound test" for headphones or analog speakers.  Clicking on the "test" buttons (front left and front right) I don't hear any sound. Despite this, the audio is working properly.  I've checked the audio levels with alsamixer; I have also checked that the test sounds actually exist in /usr/share/sounds/alsa.  I tried an installation of Ubuntu 12.04 LTS made with the desktop-cd, and in this case the speaker test works properly.  I suppose, therefore, that the problem could depend on the lack of a package, but I have not identified which one. What is better to have? A pokemon with higher IV but lower CP or vice versa? Me and my friends have encountered this situation many times. We need to decide which Pokemon to evolve. Take the following scenario:   Growlithe A: 20% more CP than Growlithe B. (898 instead of 743). Growlithe B: 26% more IV than Growlithe A. (87 instead of 69 in this case).   I didn't give more details about each Pokemon because I'd like a general answer that others can use.  Thank you kind folks!  P.S this is not a duplicate, since I understand what a higher IV interprets into.  Yes, a higher IV will define the MAX CP, but it's not the only thing to consider. A higher IV also means better chance of better moves for the evolved pokemon - and those are much more important than a high CP. Also consider that I have many Arcanines and I don't have the stardust to max them out (that is a different question). I am trying to use a Bluetooth headset on an Ubuntu PC. I am able to connect phone to pc via BT. I can stream music to PC. But cannot hear call audio. I have checked in Android phone logs, and BT sco link is established. But when making a call or virtual call (play audio through sco path in Android phone) the audio is not audible in PC headset. SCO packets are NOT appearing in btmon logs either. Anyone successfully done this?  version- ubuntu 16.04 Installed- bluez, ofono, pulseaudio pactl sink: Name- bluez_sink.22_22_8E_DE_B9_2B,             Name: alsa_output.pci-0000_00_1b.0.iec958-stereo pactl source: Name-bluez_sink.22_22_8E_DE_B9_2B.monitor               Name: alsa_input.pci-0000_00_1b.0.analog-stereo Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$