I have a function $ \frac{x+1}{x^2-3x+4} $ which I've decomposed into $ \frac{x}{x^2-3x+4} + \frac{1}{x^2-3x+4} $.  By using the definitions of even and odd functions, I know that x is an odd function, $ x^2-3x+4 $ is neither even nor odd, and 1 is a constant and constants are considered even. so my question is: is an odd function over a function neither even nor odd, still odd? Same question from an a constant (even?) function.  Thank you for your help!  Also not sure if it's relevant, but for $ x^2-3x+4 $ we obtain non-real roots, and it is also worth noting that $ \frac{x}{x^2-3x+4} $ is zero when $ x=0 $. though $ x^2-3x+4 $ is always greater than roughly $ ~1.6 $.
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.
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OP: if it were in English, would it be equally offensive?   I will write it in Dutch because you ask it so kindly.   Me: yeah, I mean what's your goal? You're just seeding hatred   OP: It is an experiment.   After that, the user changed it to Dutch.  My question is: are such statements acceptable by Stack Exchange's standards? If not, should I flag one of his posts like stated ? If yes, could you state why?  My answers to possible questions:   This happened on SO, why don't you post it on MSO?   This happened on SO but I think it's applicable to all SE sites.  Why didn't you link the user or the chat conversation?   I want the user to remain anonymous unless he or she chooses to reveal him/her self. I will give the user a link to this question  Why do you care?   I find it offensive, not only to my religion but to any religion that believes in god. I posted this question to know what you guys and girls think about this. I live by the rules, so if it's acceptable by SE then so be it and I won't bother you again.  If you don't like it then move on.   I know that this is not a mosque/church/temple and that swearing  to a certain degree. But I don't see the point in insulting god, a religion or a race in a public profile. More over, it's not even built on arguments. A word for 'independent episodes' When we have a series of episodes where every single episode depends on and develops from the previous, we may call that a sequel, or maybe a continuum.  Now let us say that we have a collection of fables, episodes or anecdotes that have the same characters, the same milieu, and the same themes; yet, this time, the episodes are NOT interdependent. They don't depend on each other in that you can watch/read 'any' one of them be it (in terms of order) from a beginning, medial, or final season, without having to watch/read the previous to understand, appreciate, and enjoy it (the one you're watching/reading). 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So, to prove $f$ is differentiable at the origin, I have to show that   $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+&lt;\nabla f(0,0),(x,y)&gt;)|}{\|(x,y)\|}=0$ But $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+&lt;\nabla f(0,0),(x,y)&gt;)|}{\|(x,y)\|}$ equals  $\lim_{(x,y) \to (0,0)} \dfrac{|(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})-(x+y)|}{\|(x,y)\|}$. I don't know how to show this limit equals $0$.  For the second part (I've only analyzed $\dfrac{\partial f}{\partial x}$ since both cases are the same), what I did was try to show that $\lim_{(x,y) \to (0,0)} \dfrac{\partial f}{\partial x}(x,y) \neq \dfrac{\partial f}{\partial x}(0,0)$   I thought of considering the curve $\phi(t)=(t,0)$, so   $\lim_{t \to 0} (f\circ \phi)(t)=\lim_{t \to 0} 2t\sin(|t|^{-1})-\dfrac{t\cos(|t|^{-1})}{|t|^{-1}}$. But $\lim_{t \to 0^{+}} \dfrac{t\cos(|t|^{-1})}{|t|^{-1}}=\lim_{t \to 0^{+}} \cos(\dfrac{1}{t})$ and this limit doesn't exist, so the original limit doesn't exist. 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We know that any field/ring of characterisitc zero must have infinite elements, but I am not sure what happens above. How to show that the set of points of continuity is a $G_{\delta}$ I found a better proof for a theorem than a proof from a published paper. Is it possible for me to publish my proof with the same theorem citing that paper? Chrome: Site has updated in the background I keep getting these notifications despite not having an RT tab open. What gives? Seo: Change the title of a page Lets say my website looks like this:  News -Hello world -Foo -Bar  So the parent page will list the last 3 news messages. For each news message there is a sub-page. For the parent page I was thinking of setting the page title to: News - Hello world, Foo, Bar.  Now if somebody adds a new message the title tag will also change. I googled this and read a few blog posts where people said that changing the title actually hurts the ranking of that page.  So is this true? 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My 1.12 solution can be found . When trying to update command blocks to 1.13, I have the following:  scoreboard objectives add invert dummy   (run at start) then:  scoreboard players set FakePlayer invert 1   (impulse unconditional repeat) chained into:  execute at @e[tag=summoned] run scoreboard players reset FakePlayer invert   (chain unconditional repeat) chained into:  execute if score FakePlayer invert = 1 invert run say "All summoned animals are dead!"   This should reset FakePlayers score continuously until all entities with tag "summoned" are dead, then it should run the final condition. This does not happen, and I can't see why.