/sci/ - Science & Math

[Anonymous No.3747714]

[Anonymous No.3747736]

x^2-2ax+b^2-y^2=0

Boring

[Anonymous No.3747745]

>>3747736
nope

r u rebardet

[Anonymous No.3747752]

>>3747736
>did not even solve problem
>boring

[Anonymous No.3747762]

<span class="math">
\pm\sqrt {y^{2}}-b^{2}}+a = x_1,2
[/spoiler]

[Anonymous No.3747765]

\pm\sqrt{y^{2}-b^{2}}+a = x_1,2

[Anonymous No.3747766]

>>3747736
Sorry, I miss an a^2.

It's boring because it's a second degree ecuation. Use the regular shit to solve them

[Anonymous No.3747769]

<span class="math">
\pm\sqrt{y^{2}-b^{2}}+a = x_1,2
[/spoiler]

[Anonymous No.3747772]

<span class="math">
\pm\sqrt{y^{2}-b^{2}}+a = x_{1,2}
[/spoiler]

[Anonymous No.3747775]

Let us note a few things (assuming we're dealing with reals)

clearly, y>=0, since we have the positive square root, and hence, y>=b, thus y^2>=b^2

Then y^2-b^2=(x-a)^2

then x=a+/-sqrt(y^2-b^2)

[Anonymous No.3747794]

(y^2-b^2)^(0.5)+a=x

[Anonymous No.3747805]

>mfw when people put +/- infront of a root because they dont realise a root naturally have 2 results

[Anonymous No.3747812]

>>3747805
but it doesn't you retard.

The square root function is defined to be the positive result.

Otherwise, it isn't even technically a function.

Learn to not be an idiot

[Anonymous No.3747814]

>>3747805
>mfw people don't put +/- in front of a root because they aren't aware it's a function and functions only return one value

[Anonymous No.3747818]

>>3747805

[Anonymous No.3747819]

>>3747805

>Mfw you use symbols and facial expressions to communicate and think
>Mfw you dont deserve a face you autistic and elitistic idiot

[Anonymous No.3747825]

The +/- it's courtesy

[Anonymous No.3747821]

>>3747805
The square root symbol only refer to the non-negative root. People like to work with functions with real arguments and real values. If you want your functions to work on sets, I don't mind, it's helpful at least for the "converse" operation, but that's not what the sqrt symbol does.

[Anonymous No.3747837]

>>3747825

No, a function can only return one value faggot.

A square root will never return a negative number, so you can't take the fucking negative root niglet.

[Anonymous No.3747843]

>>3747821
This answer is the only answer to >>3747805 that is aware of the fact that a function can return several reals if it is a function from P(R) to P(R) (or from R to P(R)), where P(R) is the set of subsets of R. It is COMMON to do that, for instance when you define, for a function f from R to R, the function <span class="math">f^{-1}[/spoiler] from P(R) to P(R) such that <span class="math">x\in f^{-1}(S)\Leftrightarrow \exists y\in S;y=f(x)[/spoiler]

[Anonymous No.3747859]

>>3747805
fuck off assburgers

the +/- is calculator friendly

[Anonymous No.3747873]

>>3747843

nigga please stop mashing your keyboard you are not impressing anyone

[Anonymous No.3747877]

>>3747873
I'm trying to educate, I don't care about anonymously impressing people. When I want to impress people, I try to use a recognizable identity.

[Anonymous No.3747898]

a function can return more than one value. don't be confused with one-to-one function.

[Anonymous No.3747902]

x = y-b+a

[Anonymous No.3747910]

>>3747898
>definition of a function: an ordered triple of sets, written (X, Y, F), where X is the domain, Y is the codomain, and F is a set of ordered pairs (a, b). In each of the ordered pairs, the first element a is from the domain, the second element b is from the codomain, and a necessary condition is that every element in the domain is the first element in exactly one ordered pair.

>every element in the domain is the first element in exactly one ordered pair
>exactly one

[Anonymous No.3747916]

>>3747898
kids today are just used to calculators and excel. They dont know fundamentals

[Anonymous No.3747937]

>>3747843
Maybe you could answer my second question in this thread
>>3747820

[Anonymous No.3748002]

>>3747937
Done: >>3747998

[Anonymous No.3748026]

>>3747910
There are different wordings. What you define here, some people call "application" or "1 to 1 function". Some people call "applications" or "functions" the generalized case where you forget about the uniqueness of these pairs. Another possible path to functions with several values is to use 1 to 1 functions, keep the domain X, but change the codomain Y to the set of subsets of Y. You then obtain 1 to 1 functions that return, for each element of the domain, exactly 1 element, but that element is a set and can therefore contain several elements of Y.

[Anonymous No.3748099]

>>3748002
Thank you so much you really helped

[Anonymous No.3750549]

>>3748026

[Anonymous No.3750583]

>>3750549
He's just being a total assburger, I know what he's actually saying. He's saying that it's easy to construct a single valued function in set theory which can act, in a way, as a function which returns multiple values. You make the outputs of the function sets of values, instead of just single values, and that whole set is the output of the function.

In practice nobody does anything like this for analytic purposes, so that poster is 99% talking out his ass.