Some common questions from the many student users of Wolfram|Alpha include “Isn’t cbrt(-8) = -2?” and “Why doesn’t the plot of the cube root include the negative part?” The answers are that -2 is just one of the three cube roots of -8, and that Mathematica, the computational engine of Wolfram|Alpha, has always chosen the principal root, which is complex valued. More generally, odd roots of negative numbers are typically assumed to be complex. You can see this in the output of (-8)^(1/3). More »
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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:
