function analysis question

[luisphysics]

(12-05-2015 01:22 PM)quinyu Wrote:  No, I want the calculator to tell me where it can interpret the function. That's the domain. I want the calculator to tell the domain of an arbitrary function f(x). What I showed was an example. Also, I want the calculator to tell the range - that is, the set of all the values that f(x) has, on the domain. How do I do this?

For your info, on the TI-nspire CAS, the command domain(asin(sqrt(x)),x) results in the output 0<=x<=1, which is what I'm looking for. (This is not the precise input but close enough to it.) While it cannot directly find the range (or at least I know of no method to do so), if I set x=asin(sqrt(y)), and have it solve for y, gives y=(sin(x))^2 (that is the inverse function), with the requirements that sin(x)>=0 and -pi/2<=x<=pi/2. From that point on, I can get a domain again for (sin(x))^2, which is obviously any real number, so that bit is irrelevant. If I solve for the other criteria, it gives max(-pi/2,2*n1*pi)<=x<=min(pi/2,2*n1*pi+pi) as a result. For the principal value (that is, n1=0) of the expression, that means that 0<=x<=pi/2. This is therefore our function range.

So, how do I execute the same sort of procedure on the HP Prime?

This may not be a satisfactory answer, but I believe the Ti-inspire has a built in option for imaginary or real inputs. If it is set to real, then the range for SINE or COSINE can be easily hard coded into the software. By definition Sqrt(x) where x <0 is imaginary, then it knows to spit out only the real part because it is set to spit out the real part. So the TI guys probably made a program to define the domain of functions, and formatted it all pretty.
Try domain(arcsin(sqrt(x))*1/((.5-x)*(.6-x))

And then the TI inspire CAS throws out a yellow triangle telling you....OHHH no be careful I'm guessing but if it gets harder than this I may be wrong.
That is what I have found the yellow warning triangle means.
This tells me that they have hard coded some stuff in the TI inspire CAS. Or have some basic algorithms to catch common items.

A calculator is a good teaching tool and "I agree that the HP Prime should have a domain function build in". In a way it does, if you plot the function, then press the Num key it will tell you the NaN which is out of bounds and it will give you values for stuff in bounds.

What I'm getting at is that the HP Prime might not do that by default for you, but you can program it to spit out the text and format it the way you want.

If your function in complex enough, use the right tool for the job. Use Wolfram alpha.