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7:39 PM
waves
 
So it's inverse functions and I'm confused about how my math teacher was doing it
reviewing for finals- also having breakdowns :(
 
do you understand inverse functions conceptually?
 
Anyhow
@bobble Yeah. I'm just confused how she solved it
conceptually, f(a)=b; then f^-1(b)=a
and f'((f(x))=x
and vice versa, f(f'(x))=x
 
okay, so what specific problem are you having trouble with?
 
So the scenario is f(x)=ax+b and f^-1(x)= bx+a. What are the values to a and b?
So first here's how far I got:
f(f'(x))=x; so f(f'(x))=a(bx+a)+b=x
abx+a^2+b=x
And I'm lost in what to do next
 
7:43 PM
well you could do f'(f(x)) = x
 
Right I did that too which is
b(ax+b)+a= bax+b^2+a=abx+a^2+b=x
abx cancels out
a^2+b=b^2+b=x. Still doesn't really help
a^2+b-b^2-a?
 
a trick that might help: these equations must be valid for any value of x
therefore, you can set x to any value you please
 
Ohhhh
That's why she replaced x with 1
Okay that's where I was mostly confused on. I think I got the rest now
 
the "set x to a convenient number" trick is one to watch out for
yay! Tutor Bobble helped :D
 
Actually, quick question
So I'm following a slightly different solving method
 
7:49 PM
and?
 
and basically we come to (x/a)-(b/a)=bx+a
so replace x with 1
 
another possibility is replacing x with b
 
0 = b^2 + a
a = -b^2
substituting might help?
 
Well she paired the stuff up
So she paied x/a=bx or 1/a=b and -b/a=a and I don't know why
 
7:51 PM
okay, warning that I might have to be rambly to explain this
these equations must be true for any value of x
therefore the coefficients of x must be the same
and the constants must be the same
 
it's analogous to imaginary-number equality
 
if it helps to think in imaginary numbers, just set x = i
 
Because the x has to be the same, the value that x be multiplied by must be the same in order for the solution to be equal
No, that makes sense
Okay last set of question
I just need a pointer in where to start
f(x)=(1/2)x+2
f(2f(2f(2z-1)))=5/2
what is the value of z?
Where do I start?
 
7:53 PM
z?
where is z?
do you mean x?
I would start by just plugging in
f(2z - 1) = 1/2 * (2z - 1) + 2
multiply that by 2
plug the result into f again
multiply that by 2
 
Hold on I'm confused. Oh I see
 
plug the result into f again
and voila, one-variable algebra with z
 
Oh. Ohhh I see what you're doing/ Thank you
I will leave your lunch in peace now
 
sometimes plug-and-chug is the only way to solve a problem
 
Plug-and-chug
 
7:57 PM
by the way I don't think you've seen this:
in [grid-deduction] Puzzle Solving, yesterday, by bobble
I was greeted (when I got back from biking) with an email saying there was an update on reach-school application, so I logged into the portal, navigated through several links, and finally found a standard rejection letter. :(
 
Awwwwwww
I'm so sorry :/
And i haven't seen anything in the last 2~3 days, so you're going to have to update me
 
well that was basically my news
 
Ah
Good news, I'm not failing math anymore!
 
@bobble :(
 
yay!
 
8:02 PM
I was at a D+, but I got a 88.9% on my last test so I'm at a C- now
 
that is Good News
 
smh I can't believe I'm celebrating that I have a C- in a class
Hmm
I need some help again but bobble is gone
 
on inverse functions?
 
Kind of
Oh actually my teacher posted videos on it
 
some problems solve themselves :)
 
8:11 PM
Hehe, that's a nice way to put it
 
handy hint for general problem solving - if you're stuck, try explaining the problem to an imaginary person (or inanimate object), often following a more coherent thought process gives you the "aha!" moment
in Software Engineering, we call the "rubber ducking", because traditionally you have a rubber duck on your desk whom you explain the problem to
 
Oh, is it like the rubber ducky jokes in coding
^
I currently don't have a rubber ducky, on me, but I do have this rubiks cube
 
I also like ducks, so it's a win-win for me :)
then help the Rubik's cube become an expert! :P
it feels silly at first, but you'd be amazed at how immensely helpful it is
 
Well my mom's currently downstairs, so maybe when I'm alone one of these days
she might think I've gone mad
 
or just explain to her what you're doing :)
 
8:17 PM
hehe
 
also, to your earlier point - the educational grading system has the unfortunate habit of being stuck in a negative-weighted paradigm, one day I'm hoping this will change (I'm trying to start doing that here in NZ), but the way I would look at it, don't celebrate getting a C- in class, celebrate that you improved a whole grade!
 
True
I hate how everything is graded in math this year
My grade is basically solely based on tests (multiple-choice, no partial credit) and occasional free participation points which do give a really solid cushion but like
 
it's an unfortunate, and archaic, system :( I feel you
 
I can usually get by in some of my other classes. Like in AP Physics, my teacher gives you a point for trying to solve the problem, another point for doing the steps correctly, and another point for getting the answer correct
(for FRQs)
What's the most frustrating is losing an entire point just because I messed up a number somewhere while having the right idea
Like I thought that tan(120) was sin(1/2)/cos(sqrt(3)/2) which I get if I wrote that in a unit circle test, but this was for like angle addition
Getting the correct numerical value was just one step
Ugh
 
yup, and there are so few places in life where you're expected to perform under the same sort of circumstances - I love learning but hated how school assessed your capabilities - only thing I can say is that one day it'll be behind you and you'll get to do the things you enjoy :)
 
8:27 PM
I don't know. It's like why is math the one class where I'm tested like this
 
unfortunately I've got to step out for a meeting, so will be AFK for at least an hour. All the best with your study! :D
 
 
1 hour later…
9:39 PM
@bobble what is ⨂ sybol?
 
XOR, I think
 
oh maybe no?
 
I have never learned XOR before
 
1
A: Meaning of symbol product (cross) in a circle: ⨂

TeunI assume $\mu$ and $\nu$ are distributions with $d\mu$ and $d\nu$ the corresponding measures. Then $d\mu\otimes d\nu$ denotes the product measure. Distributions $\mu$ can be seen as generalised functions, where $\mu(x)$ doesn't have to be defined. However, I think in your case $\mu$ and $\nu$ are...

 
9:40 PM
it's the product of two matrices
 
oh, they're defining the thingy as an operation
 
Is it just r*s and they didn't want to confuse X as a variable??
 
You could think of it as a function ⨂(r, s) = sr + s - r - 1
(with ⨂ being a two-variable function)
 
9:42 PM
yeah, the function analogy is perfect
they have "invented" an operation, so to speak
 
Oh that whole thing is a function?
@Dmihawk Ah, okay thank you. That makes sense
 
basically they defined a function, and now they're asking questions about that function
they're just doing it in an annoyingly complicated mathy way
 
It's saying we have r and s operated as r⨂s it is sr + s - r - 1
 
precisely :)
 
hey look I think you have a fourth tutor
 
9:44 PM
similar to how r^2= r*r, except that's not what ⨂ means, but just for this scenario
 
wait fifth
me, Deus, Gareth, Bubbler, Dmihawk
 
Wow. I have an entire gang of just ppl as tutors
 
I'm far better at Physics and Chemistry if you take those subjects, but I dabble in mathematics from time-to-time
always happy to help out when I can :)
 
Well, I'm assuming you've graduated and have taken much harder math classes than I have so far, so none of these questions should be very complex
At least, compared to what you've learned.
 
I have (semi) competently tutored Math, Chemistry, Biology, English, History, and Computer Science
 
9:47 PM
my Bachelors degree is in Software Engineering, so while, yes Math was part of it, now I just write software that does Math for me :P
 
(to be fair the Computer Science was just the intro class and then AP CS A)
 
How can S not equal 1 in this situation what???
 
what if s = 0?
 
Hm, perhaps? I'm just trying to solve it by isolating r instead
 
well if s = 0 then you only have -r - 1 = 0
poof, r is almost isolated
 
9:52 PM
But what if s isn't equal to 0?
 
... I didn't say that s=r anywhere??
I don't think it works if s can't be 0 or 1
just a guess
 
Well I'm less inclined to randomly guess that s is 0, that's all
 
working from 0 = sr + s - r - 1, start rearranging to isolate
1 = sr + s - r
1 + r = sr + s
1 + r = s(r + 1)
 
Right. That gets s=(1+r)/(1+r)
 
1 + r / (r + 1) = s
 
9:55 PM
but you can't divide (r + 1) away if it equals 0
 
Wait. Maybe r=-1?
 
that works yes
 
Well my logic is
If r=-1, then 0/0 is undefined
That's the only time where the value for (1+r)/(1+r) doesn't equal 1.
And we know that r=-1 has to be the answer, because it says that s=/=1
Bam
"Q.E.D., checkmark, and a big fat smiley face"
 
:D
stepping out again (ugh)
 
That was kind of satisfying
 
10:22 PM
Ooh, looks like some math happened in here :D
 
there was math
also grid-deduction room is currently Deus + me attempting a Fillimino
 
Nifty :)
Hopefully day is going well?
 
day is good and bunnies ripped up their box
 
Aww, bunnies <3
 
so annoying when work gets in the way of puzzling :P
are there photos of said bunnies?
 
10:36 PM
Hang on, I will find one they posted a few days ago
here is one of bunnies cuddling
 
there is another one where they're trying to fit into a box, but one can't fit and its butt is sticking out and it's the cutest
i can't find it right now
 
2 days ago, by bobble
user image
here you go
 
BUNNY BUTT <3
 
I searched your messages for "butt" and then looked for the picture nearby
 
10:38 PM
awwwwww they're adorable :)
 
"I searched your messages for 'butt'" made me crack up
 
user image
3
this is my little puzzle-solving buddy
 
KITTY
 
awwwww
 
what is cat's name??
 
10:41 PM
i love black cats - they're so underappreciated
 
officially "Jetson", we call him "Jet" and I seem to give him a new nickname every day haha :P
@Deusovi we do too! :D
 
Black cats and patchworks are my favorites <3
 
do you have a witch hat for kitty?
 
no, but that sounds like an amazing idea!
my wife just said I should have put a cuter photo of him rofl
can I sneak one more kitty pic in?
 
yes
 
10:44 PM
 
i would die for him <3
 
speaking of kitties, dad's friend's kitty is ... not very nice
ironically, her name's Fuzzy
(her = cat, not friend)
 
Finding some pictures of my pupper to trade, hang on
this is my baby
 
(oh and i just noticed the edited room description lol)
 
nawwwwwww
 
10:46 PM
it da pupper
 
so adorable <3
 
^
 
you should see Deus's cat too, absolutely precious <3
 
go on Deus :)
 
ooh hold on
 
10:48 PM
Sciborg kidnapped Deus's cat once
 
i did not kidnap kitty, i merely borrowed it
 
this is nala! she only has three legs but we don't think she's realized it yet
 
look at that fluffy baby!!
 
in The Sphinx's Lair, Nov 28 at 23:45, by Sciborg
HELP US WITH THE PUZZLE OR I'LL GIVE HER EXTRA SNUGGLES
explain this then
 
she's gorgeous! <3
 
10:49 PM
@Sciborg potayto potahto
 
Nala and Jetson are the cutest cat names too
 
the foster family we got him from named him the same week SpaceX were doing a bunch of stuff, so he and his brother got space-themed names (iirc, his brother is 'Orbit')
 
awww that's cute
 
AWWW
 
well we've thoroughly hijacked North's room now, although I can't imagine anything more therapeutic than photos of amazing rabbits, cats, and dogs :)
does anyone have ducks/ducklings? and if so, can I come and live with you? :P
 
10:54 PM
i am perfectly okay with our hijacking the room for animal pictures :p
no ducklings here, but i had some fish and snails in college
 
@Deusovi This is like Deja Vu
 
yeah i've said something like that before
 
Those exact word, actually
 
Have we finally confirmed that Deus is a highly superintelligent AI? it would explain so much
 
that's how i always describe her because it's pretty accurate
 
11:00 PM
it is adorable and we love her
 
stepping out for lunch, back later :)
 

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