Solve Domain and Range of a Function with Wolfram|Alpha
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:
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:
We might ask for the domain and range of a function involving an inverse trigonometric function:
Or we might be interested in an algebraic function of several variables:
We hope you like this new functionality and encourage you to keep the suggestions coming!