Domain of x^(1/3) +x^(4/3): Why Negative Values Not Allowed?

[CalculusHelp1]

Homework Statement

Graph x^(1/3) +x^(4/3)

Homework Equations

Limits, derivatives, etc.

The Attempt at a Solution

Hi guys, I was attempting this problem and then verifying it using a function grapher online. I noticed that all of the function graphers do not plot the function for avalues of x less than 0, and my calculator also gives an error when attempting a negative number to the power of 4/3. I would assume you can raise a negative number to the power of 4/3, so why does the calculator give an error and the function graphers so that negative x is outside the domain? Any ideas?

 

[micromass]

Ah yes. Well, most of the function graphers treat 1/3 as 0.333333333... So they don't consider 1/3 as a fraction, but as a real number instead. But a negative number exponent a general real number does not have to exist. It only exists if this real number is a fraction. But function graphers fail to see that it IS a fraction. So it's really because function graphers are stupid...


I would suggest following (free) program which circumvented the problem and which would graph your function correctly: http://www.padowan.dk/graph/

 

[CalculusHelp1]

That's much better, thanks for the help.