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+--- Thread: [CAS] find domain for function? (/thread-4727.html)
[CAS] find domain for function? - ww63 - 09-16-2015 10:46 AM
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
RE: [CAS] find domain for function? - ww63 - 09-18-2015 01:20 PM
Just bring it on top again!
@parisse: Is there no such command?
regards Wolfgang
RE: [CAS] find domain for function? - Tim Wessman - 09-18-2015 01:42 PM
There is not. He feels it is not a useful thing to have.
RE: [CAS] find domain for function? - Han - 09-18-2015 02:10 PM
A graph would serve the same purpose as such a command, and would be more useful from a pedagogical point of view.
RE: [CAS] find domain for function? - Helge Gabert - 09-18-2015 02:11 PM
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!
RE: [CAS] find domain for function? - parisse - 09-18-2015 03:37 PM
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.
RE: [CAS] find domain for function? - Aries - 09-19-2015 08:23 AM
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 ;-)
RE: [CAS] find domain for function? - teerasak - 11-13-2019 09:49 AM
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
RE: [CAS] find domain for function? - Aries - 11-14-2019 09:00 AM
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
RE: [CAS] find domain for function? - teerasak - 11-14-2019 11:20 AM
@ 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
RE: [CAS] find domain for function? - CyberAngel - 11-15-2019 01:34 AM
(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)
RE: [CAS] find domain for function? - Aries - 11-15-2019 09:43 AM
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
RE: [CAS] find domain for function? - cyrille de brébisson - 11-18-2019 06:06 AM
hello,
Doesn't tabvar solve your problem?
Cyrille
RE: [CAS] find domain for function? - Aries - 11-18-2019 12:13 PM
Well, of course it does
Best,
Aries
RE: [CAS] find domain for function? - lrdheat - 11-20-2019 04:01 AM
tabvar is one of my favorite items on the HP 50g, and on the Prime!