[CAS] find domain for function?

[ww63]

Hello,

is there a function / command to find the domain, for whitch a function is defined?

Examples:

f(x) = x/(x-1) should result in x<>1
f(x) = ln(x) should result in x > 0

regards Wolfgang

[ww63]

Just bring it on top again!

@parisse: Is there no such command?

regards Wolfgang

[Tim Wessman]

There is not. He feels it is not a useful thing to have.

[Han]

A graph would serve the same purpose as such a command, and would be more useful from a pedagogical point of view.

[Helge Gabert]

BTW, The 50G has TABVAR, which returns the domain and poles for some functions (reducible to a rational expression), but I never found that particularly useful either. Easier to just graph the function!

[parisse]

Xcas has the singular function, it does not return exactly the domain (for example singular(ln(x)) returns [0]), but it gives some informations about.

[Aries]

As for polynomials functions there is no problem, their domain is R.
For fractional functions 1/f(x) we can solve f(x)=0 and the roots are the ones to be excluded from R.
For irrational functions sqrt(f(x)), solving f(x)>=0 is enough.
In many cases in order to find the domain of a function we need to set a system:
y=sqrt(log(x^2-8*x+8)), solve({x^2-8*x+8>0,log(x^2-8*x+8)>=0}) and that's all !!!
Domain found !!!!!
Algebraically, not graphically B-) ^_^
Best,

Aries ;-)

[teerasak]

Perhaps with past release of firmware, it could not do so.

With the latest release (2018 10 16), I found domain command which can be used to find domain:

For example, to find domain of f(x) = 1/(x-1), simply use:
domain(1/(x-1),x)
it will return x<>1

I'm just thinking howto find range of this function. Perhaps the following command can help:

domain(solve(y=1/(x-1),x),y)
it will return y<>0

[Aries]

Not all functions are invertible in their domain, y=x^2 is non-invertible in its domain.
What if f(x) is non-invertible ?
A function f is invertible if and only if it's injective, that is whenever f(x)=f(y), x=y.
In certain cases restricting domain of f(x) could make it invertible.
Best,

Aries

[teerasak]

@ Aries

You can use domain(solve(y=x^2,x),y). The calculator will give result y>=0

However, this may not work with implicit function e.g abs(x) + abs(y) = 4

[CyberAngel]

(11-14-2019 11:20 AM)teerasak Wrote:  @ Aries

You can use domain(solve(y=x^2,x),y). The calculator will give result y>=0

However, this may not work with implicit function e.g abs(x) + abs(y) = 4

Would it help to set:
assume(x>=0)
assume(y>=0)

[Aries]

As for the image (range) of f it's supposed to work with implicit functions as well but I suggest drawing a sketch or looking for maximum and minimum of y or even analysing f.
Best,

Aries

[cyrille de brébisson]

hello,

Doesn't tabvar solve your problem?

Cyrille

[Aries]

Well, of course it does
Best,

Aries

[lrdheat]

tabvar is one of my favorite items on the HP 50g, and on the Prime!