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# Domain and range of f(x) = cube root x?

The answer is the set of real numbers, right? WolframAlpha gives x>=0 and y>=0, and I can't figure out why it gives this result.

### 3 Answers

- RaffaeleLv 78 years agoFavorite Answer
Windows calculator, too, gives error when trying to get cube root of (-8) as well as my calculator

and Wolfram Alpha, too

http://www.wolframalpha.com/input/?i=cube+root+-8

but ∛(-8) = - 2, as we all know since middle school

the reason why calculators and Wolfram give error is that domain and of x^y is assumed to be R+ (0 excluded)

it is a good reason because if in x^y you let x to be negative, each rational exponent with even denominator would not exist in R!

Anyway x^3 is invertible on R, therefore

domain and range of cube root are R

- 8 years ago
The square root of a negative number is undefined, therefore the range is y>0 for f(x)= square root x. But the cubed root of a negative number is a real number, so the graph ends up reflecting over the origin making the domain and range all real numbers