inverse function command
10-07-2017, 04:20 PM
Post: #1
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
inverse function command
Function Example:
y:=1/(sqrt(2*x-3));

Needed is a built in command to essentially do this:
simplify(solve(x = (1/(sqrt(2*y-3))),y))(1); // ==> (3*x^2+1)/(2*x^2)

In other words, a direct command that will return the inverse function of a function argument.

-Dale-
10-07-2017, 06:53 PM
Post: #2
 Joe Horn Senior Member Posts: 1,687 Joined: Dec 2013
RE: inverse function command
(10-07-2017 04:20 PM)DrD Wrote:  Function Example:
y:=1/(sqrt(2*x-3));

Needed is a built in command to essentially do this:
simplify(solve(x = (1/(sqrt(2*y-3))),y))(1); // ==> (3*x^2+1)/(2*x^2)

In other words, a direct command that will return the inverse function of a function argument.

solve(y=1/(sqrt(2*x-3)),x) does the job (and even returns the result simplified if you have the "Simplify" CAS Setting on Maximum). Do you want something simpler than that?

<0|ɸ|0>
-Joe-
10-07-2017, 08:24 PM
Post: #3
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
I do want something simpler than that. There is a lot of use for inverse functions in math education. This, alone, should justify having a dedicated command that simply takes a function and returns it's inverse function. We have commands on the prime that are far less commonly used, and one command that seems to indicate that it WOULD be useful for inverse functions (according to the help docs), but isn't.

The solve command has many discussions in the forum, and has been frustrating. It takes additional presence of forethought to relate the idea of obtaining an inverse function, by using a solver.

So yes, a new command, perhaps invf(Func), would be useful, especially for students learning calculus. I would envision such a command to also return a simplified result. This would allow students to quickly confirm intermediate results and verify problem solution progress.

I could create a program for this, which would be contrary to one of the benefits of purchasing a powerful hand held calculator designed for students and educators. Ideally, as I encounter math problems, I want a device with an easy to understand, fully capable interface, that is up to the tasks required. That is where the value is for me, as a calculator customer. It's more than just the pride of ownership, I want the utility value.

-Dale-
10-08-2017, 12:21 AM
Post: #4
 Joe Horn Senior Member Posts: 1,687 Joined: Dec 2013
RE: inverse function command
How do you teach a student to find the inverse function of y=f(x) by hand? Isn't it by solving that equation for x (that is, isolating x on one side of the equation)? And it teaches what an inverse function IS, and exercises the student's algebraic skills. After learning it that way, using SOLVE to find inverse functions would come naturally.

That seems far more educational than telling the student, "just press the InverseFunction key; it lets you get the answer without requiring you to understand what inverse functions are, or anything else for that matter."

Disclaimer: The above was my opinion when I wrote it, but might no longer be my opinion by time you read it. I reserve the right to keep learning and to adjust my opinions accordingly.

<0|ɸ|0>
-Joe-
10-08-2017, 01:11 AM
Post: #5
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
By that reasoning a student shouldn't use technology during the educational process. You could use similar rationale for advanced education and on into career and retirement. Thanks, just the same, but I prefer to use the prime for educational advantage. Somehow it seems obvious that the use of these implements makes education faster, easier, and better. Which is why an inverse function command is a good idea, in my opinion, which may also change, if I get a different opinion of that opinion.
10-08-2017, 02:35 AM
Post: #6
 Joe Horn Senior Member Posts: 1,687 Joined: Dec 2013
RE: inverse function command
Just thinking out loud...

I see your point, and certainly agree on the educational value of technology, having taught high school math with HP calculators for decades. Perhaps my unspoken fear is the "slippery slope" of portable CAS systems, approaching the limit of voice recognition of every kind of problem and instant output of the solutions, requiring the user to know absolutely nothing. That would be a great tool in the field (!), but a TERRIBLE thing to teach with. No learning happens at all when the students have technology at hand which can do all their homework and take their tests for them, thus eliminating all incentive they may have to learn anything.

However, learning does happen in stages, so learning happens best when students have technology at hand which is optimized for learning exactly what it is that they are learning at that stage. Will somebody ever design a handheld which adapts itself to the student's current stage of math learning? Maybe. But nobody has done it yet.

<0|ɸ|0>
-Joe-
10-08-2017, 04:07 AM
Post: #7
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
Totally agree. I have heard that robotic teaching, with adaptive teaching methods tailored to each students individual learning rate, is already being developed. So technology is just getting started in educational fields.
I wonder if hp will be building any of that hardware?
10-08-2017, 04:18 AM
Post: #8
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
Incidentally, where is the greater hurt? Typical conventionally educated person, that doesn't remember unused details after education, or technology based education, wherein one immediately gains useful solutions, and can derive value instantaneously, at any point in time?
10-08-2017, 06:33 AM
Post: #9
 parisse Senior Member Posts: 1,136 Joined: Dec 2013
RE: inverse function command
(10-08-2017 04:18 AM)DrD Wrote:  Incidentally, where is the greater hurt? Typical conventionally educated person, that doesn't remember unused details after education, or technology based education, wherein one immediately gains useful solutions, and can derive value instantaneously, at any point in time?
There is a high risk of replacing teaching how to do it with your brain by teaching how to press a succession of keys, where the succession of keypress will not be valid anymore in a few years because UI will have changed. This can also happen with a builtin command because the name might change, and there is a good reason why there is no universal commandname for that:
1/ there is no magic way to invert any function (solve can not solve symbolically any equation)
2/ even if solve can solve the equation, there might be several solutions, and no way to choose one.
I can extend @@ (compose power) to negative exponents by inverting a function if solve can solve the equation (choosing the first solution), but I'm not convinced it will be better.
10-08-2017, 10:09 AM
Post: #10
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
There is a tendency to move away from the idea of keypress technology. In time, other methods, including a biological interface, may become practical. Regardless of the technology in place as of a certain time, the idea of information processing using advanced technology is worthwhile.

Using a shopping cart, is better than carrying many items by hand, to the check out stand, possibly needing to go back for more. Hand carrying those items helps to assure ones memory where each product is within the store, but getting in and out of the store faster, is more efficient and results in greater sales volume.

There is a parallel in information technology. It's also inevitable at this point, isn't it? Students already have an option of stay at home (on line) education. That wasn't an option during my experience. Technology is pervasive in the classroom, including devices like the smartphone, and problem solving by example, is more visually and conceptually understandable, using multimedia. I don't see much argument against the idea. Keypress limitations, (as you describe) are but a mere moment on the scholastic timeline.

I agree that the solve command isn't ideal. In fact, the whole idea of calling inverse functions, inverses, is pretty lame. I mean if f(x) is a valid function, calling it's inverse f^-1(x), is just crazy, there is no mathematic recipropral in play there, (no exponent of -1, by the laws of exponents). That's what we call it, and in any event, it would be helpful to have a built in command to accommodate deriving so-called inverse functions.
10-08-2017, 12:07 PM
Post: #11
 parisse Senior Member Posts: 1,136 Joined: Dec 2013
RE: inverse function command
I'm sorry but your arguments are too elaborate for my poor level in English.
10-08-2017, 01:02 PM
Post: #12
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
I'm sorry for language issues. Technology is a good thing. It should be easy to use, and powerful. Using technology enables learning at a faster rate. Some American students, are using online courses as part of their regular classroom studies.

Who knows what tomorrow brings? It's ok if keypress technology goes away, something better will replace it. Some math teachers are terrible spellers, and some English teachers can not help solve math word problems! Both are well educated. Sometimes what was learned can be forgotten in time. Technology, in some form, will likely be able to help educators, students and others, recall forgotten details better.

Thank you for your help. I appreciate your help, and I hope others do also. Sometimes the prime can be difficult to use. My intention is to help identify areas where the prime seems like it could be improved. I use the prime quite often. Because I use it so often, I find problems where the prime isn't good. Often, it is my fault, and sometimes I'm pretty sure the prime could be improved.

I seek a built in inverse function command, that would be helpful for related problems. It should be an easy command to find in the toolbox, with understandable help documentation.
10-08-2017, 01:32 PM
Post: #13
 Joe Horn Senior Member Posts: 1,687 Joined: Dec 2013
RE: inverse function command

There is nothing new under the sun.

<0|ɸ|0>
-Joe-
10-08-2017, 01:41 PM (This post was last modified: 10-08-2017 01:43 PM by DrD.)
Post: #14
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: inverse function command
Those keys do look like they have been under the sun, (perhaps too long)!
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