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Mark McClure

Solve Domain and Range of a Function with Wolfram|Alpha

February 21, 2012 —
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Wolfram|Alpha has been steadily growing since its initial release nearly three years ago, and this growth is directed, in part, by the queries it receives. For example, the Wolfram Education Portal was created largely in response to the obvious demand for Wolfram|Alpha in the classroom. As a more specific example, we’ve recently enabled Wolfram|Alpha to respond to domain and range queries for real functions.

The domain of a real function is the set of real numbers that can be plugged in so that the function returns a real value. If, for example, we wish to evaluate f(x) = √(x + 2) / (x – 1), then we should ensure that x + 2 > = 0 and x – 1 ≠ 0:

Domain of √(x + 2) / (x - 1)

Note that the range, or the set of real values that can come out, is also returned, and a graph of the function helps illuminate why this is the range. Sometimes we might want to query the range directly:

Range of 1 / (1 - x^2)

We might ask for the domain and range of a function involving an inverse trigonometric function:

Domain and range of x * arccos(x)

Or we might be interested in an algebraic function of several variables:

Domain and range of f(x, y) = √(y - x^2)

We hope you like this new functionality and encourage you to keep the suggestions coming!


thx. Great job. Very useful.

PS: please add an option to like (facebook), not only share…

Posted by Unrealmirakulix February 21, 2012 at 12:13 pm

    There’s no need to add a “like” button to anything on the web. It’s an intrusive element and more people need to learn about how it actually works (so they can stop using it so liberally). Look into it and I bet you’ll be avoiding it from now on…

    Posted by John February 21, 2012 at 5:37 pm

That’s great. Unfortunately the internet and its many tools have rendered our children mindless fools who can only answer questions based on a query. I knew my multiplication tables by hard up to x12 by the time I was in GR4. Today kids in GR11 still don’t know them. Pathetic.

Posted by TheRoc February 21, 2012 at 3:19 pm

My understanding is that it is possible to do the same for multiple variables in a symbolic way. Is that true?

Posted by Carlos Ortega February 26, 2012 at 10:51 am

I cannot even imagine how much better my final math exams would have been if I just could have used a smartphone and wolframalpha … Damn ๐Ÿ™‚

Posted by Borman March 7, 2012 at 9:29 am

Great post Mark, please can You give me an example how to find domain of multiple functions? does the query go:
domain of y=x and y= 2 and..
or is the syntax different? i tried with “and”, it doesnt work. Thanks in advance!

Posted by Hrvoje August 27, 2014 at 2:47 am

a step-by-step solution to find the domain will be a great thing

Posted by res October 18, 2014 at 6:13 pm

please tell me the range of function (x+1)/(x-1)

Posted by amber October 29, 2014 at 9:57 am

As with most things, this is a great tool if one is actually trying to learn. If one doesn’t want to, there are always ways around it. Thanks for the article – this seems like a great way of checking your answers, or seeing how they relate to the graph.

Posted by Kathy W. December 2, 2014 at 2:20 pm