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Shuri2060
01/29/2022 12:18:24
Any more?
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Ansh_
01/29/2022 12:18:30
nope
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謝墨離
01/29/2022 12:19:14
Oops
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謝墨離
01/29/2022 12:20:12
Is it able to prove f(1)=1
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Ansh_
01/29/2022 12:20:47
I dunno ._. f(0) is all I can find atm
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謝墨離
01/29/2022 12:20:58
:flonshed:
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Ansh_
01/29/2022 12:21:04
I'm thinking about f(f(x)) = x atm, that's all I haven't used
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Shuri2060
01/29/2022 12:21:06
If f(1) = 1 does that get us anywhere?
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謝墨離
01/29/2022 12:21:17
I’m thinking
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Shuri2060
01/29/2022 12:21:23
how does this determine what f(pi) is
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謝墨離
01/29/2022 12:21:32
Shall I prove it’s possible when X and Y are integers
1
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謝墨離
01/29/2022 12:21:38
And I’m going to use mathematical induction
1
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Shuri2060
01/29/2022 12:21:52
yes you have enough information to uniquely determine f on Q
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(っ◔◡◔)っ ☆ n0te ☆
8900
(っ◔◡◔)っ ☆ n0te ☆
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Shuri2060
01/29/2022 12:21:57
but theres no need to do this.
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Shuri2060
01/29/2022 12:25:52
$$f(x^2)=xf(x)$$
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TeXit
01/29/2022 12:25:55
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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Shuri2060
01/29/2022 12:26:12
I'm going to suspect this allows us to extend to algebraics
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Ansh_
01/29/2022 12:27:07
Does it help if I show f(x^2) = [f(x)]^2?
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Ansh_
01/29/2022 12:27:22
Oh obviously it does.. we're done
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Ansh_
01/29/2022 12:27:23
lmao
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Shuri2060
01/29/2022 12:27:24
...
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Ansh_
01/29/2022 12:27:28
I'm so dumb 🤦‍♂️
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Ansh_
01/29/2022 12:27:44
:sad:
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Shuri2060
01/29/2022 12:27:58
I just have doubts
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Ansh_
01/29/2022 12:28:01
SO uhh apparently, I was hitting this mark
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Ansh_
01/29/2022 12:28:05
with
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Ansh_
01/29/2022 12:28:17
$f(f(x)) = x \land f(x^2) = xf(x)$
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Ansh_
01/29/2022 12:28:25
So I just...
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Shuri2060
01/29/2022 12:28:28
wait what
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Shuri2060
01/29/2022 12:28:31
the left thing
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Shuri2060
01/29/2022 12:28:32
we are done
0
1
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Shuri2060
01/29/2022 12:28:34
oh nvm nvm
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謝墨離
01/29/2022 12:28:39
Huh
1
0
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Shuri2060
01/29/2022 12:28:42
no no no continue
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Ansh_
01/29/2022 12:28:46
$f(f(x^2)) = x^2 \land f(x^2) = xf(x)$
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1
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Shuri2060
01/29/2022 12:28:56
kk
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Ansh_
01/29/2022 12:29:04
$f(xf(x)) = x^2$
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謝墨離
01/29/2022 12:29:23
And then?
1
0
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Ansh_
01/29/2022 12:29:31
And switch .. uh x with f(x) :thinkies:
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Shuri2060
01/29/2022 12:29:41
you what.
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Shuri2060
01/29/2022 12:29:48
'Let f(x) = x'
0
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Ansh_
01/29/2022 12:29:49
$f(f(x)x) = f(x)^2$
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Shuri2060
01/29/2022 12:29:49
Sure thing.
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Ansh_
01/29/2022 12:29:53
Nope lmao
0
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Ansh_
01/29/2022 12:30:01
plug f(x) in all places where x currently is
0
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Ansh_
01/29/2022 12:30:08
lol
0
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Shuri2060
01/29/2022 12:30:13
jk, keep going
0
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Shuri2060
01/29/2022 12:30:21
wait nice
0
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Shuri2060
01/29/2022 12:30:24
f(x)^2 = x^2
0
1
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Shuri2060
01/29/2022 12:30:27
asopdokpaskopddskoapdsoakpdsokpadkop
0
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Ansh_
01/29/2022 12:30:33
So $x^2 = f(xf(x)) = [f(x)]^2$
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Shuri2060
01/29/2022 12:30:40
awawaawawawwaawwa
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Shuri2060
01/29/2022 12:30:41
we did it
0
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Ansh_
01/29/2022 12:30:47
I did -_- wdym
0
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Shuri2060
01/29/2022 12:30:47
*ansh did it
0
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Ansh_
01/29/2022 12:30:49
UwU
0
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Shuri2060
01/29/2022 12:30:58
proof checking is important
0
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Ansh_
01/29/2022 12:31:00
_needs more praises_ :stareFlushed:
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謝墨離
01/29/2022 12:31:04
Oh
1
0
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謝墨離
01/29/2022 12:31:06
Hey thx
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Ansh_
01/29/2022 12:31:10
*_pats_
0
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謝墨離
01/29/2022 12:31:13
You guys
1
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Ansh_
01/29/2022 12:31:23
Btw.. some parts were unnecessary :catThink:
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謝墨離
01/29/2022 12:31:27
I love you guys
1
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Ansh_
01/29/2022 12:31:32
No lmao
0
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謝墨離
01/29/2022 12:31:32
:catblush:
1
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Shuri2060
01/29/2022 12:31:32
i did nothing
0
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Shuri2060
01/29/2022 12:31:35
but i will accept.
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謝墨離
01/29/2022 12:31:47
you just prove it
1
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Ansh_
01/29/2022 12:31:58
👀 I won't share answers though
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Ansh_
01/29/2022 12:32:35
\j Figure from the hints.. (if needed, I left the latex there)
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謝墨離
01/29/2022 12:33:24
https://cdn.discordapp.c…82346/image0.jpg
image0.jpg
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Ansh_
01/29/2022 12:33:36
Basically you only need to show: i) f is odd and hence, f(0) = 0 ii) f(f(x)) = x iii) f(x^2) = x f(x) in that order
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謝墨離
01/29/2022 12:33:37
:hype:
1
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Ansh_
01/29/2022 12:33:38
and you're done
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謝墨離
01/29/2022 12:33:44
.close
1
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9f99f6faa0c94d4ca2ccc297ddf3cf7a
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Ansh_
01/29/2022 12:33:49
:KEK:
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謝墨離
01/29/2022 12:33:56
:AWOOKEN:
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205,740
help-1
9f99f6faa0c94d4ca2ccc297ddf3cf7a
706,934,233,012,371,600
Ansh_
01/29/2022 12:34:21
@Shuri2060 thx so much >_< (_this was the first time in a whileeeeeee I'd done any functional equations on my own_)
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help-1
9f99f6faa0c94d4ca2ccc297ddf3cf7a
321,445,119,171,756,000
Shuri2060
01/29/2022 12:34:35
I can say, this has almost never happened to me.
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help-1
9f99f6faa0c94d4ca2ccc297ddf3cf7a
321,445,119,171,756,000
Shuri2060
01/29/2022 12:34:46
On the other hand, there are plenty of times when I was able to read the solutions on my own.
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help-1
9f99f6faa0c94d4ca2ccc297ddf3cf7a
321,445,119,171,756,000
Shuri2060
01/29/2022 12:34:49
.close
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help-1
62c1b01245174813bf9d8b6a5a63340c
348,696,743,388,381,200
A Lonely Bean
01/29/2022 12:35:02
:thonk:
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help-1
62c1b01245174813bf9d8b6a5a63340c
706,934,233,012,371,600
Ansh_
01/29/2022 12:35:07
Beans 👀
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help-1
62c1b01245174813bf9d8b6a5a63340c
348,696,743,388,381,200
A Lonely Bean
01/29/2022 12:35:17
What happened here
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help-1
62c1b01245174813bf9d8b6a5a63340c
706,934,233,012,371,600
Ansh_
01/29/2022 12:35:33
we solved the thing on the go :KEK:
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 12:49:53
Hey I'm still having some issue with trigonemetric functions and working with them, if I have sin(x)>=cos(x+pi/2)+2 can I just transform the cos to -sin(x) and then do + sin(x) and bring it to the other side and solve 2sin(x)>=2?
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help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 12:51:48
Yes you can
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 12:51:57
ok good
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 12:52:02
that makes a stone fall from my heart
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help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 12:52:25
You'll have to show the steps though
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 12:52:48
Yeah ofc
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help-1
62c1b01245174813bf9d8b6a5a63340c
420,244,167,726,333,950
kirby your mom
01/29/2022 12:53:01
$\cos(x) = \sin(\frac{\pi}{2} - x)$
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help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 12:53:03
**kirby your mom**
https://cdn.discordapp.c…167726333953.png
420244167726333953.png
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 12:53:17
yep and he has
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 12:53:36
$\sin(-x) = \cos(\frac{\pi}{2} - (-x))$
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help-1
62c1b01245174813bf9d8b6a5a63340c
510,789,298,321,096,700
TeXit
01/29/2022 12:53:38
**M.E.G. Yottachad**
https://cdn.discordapp.c…734008745984.png
328662734008745984.png
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help-1
62c1b01245174813bf9d8b6a5a63340c
328,662,734,008,746,000
Geopchad
01/29/2022 12:53:43
which is just -sin(x)
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 12:53:56
oh now Im confused
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help-1
62c1b01245174813bf9d8b6a5a63340c
182,418,252,830,343,170
lennygo
01/29/2022 12:54:03
sin(-x) is equal to -sin(x)?
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