why does the graph of x^(2/3) only exist on the domain of (0,infinity)?

A

Antonio

Member
why does the graph of x^(2/3) only exist on domain of (0,infinity)?

if i plugged in a negative value say, -1 (negative one)...... via 3*sqrt((-1)^2) "the 3rd root of negative one squared"....i would get an output of -1........on the otherhand if i plugged in -1^(2/3) or "negative one raised to the power of 2/3", i would get an error....Aren't they the same thing? So...

why does the function only exists on 0->infinity, why is this the case? I need a thorough explanation!!
 
D

dis_orient_ed

Member
The range of x^2 is only positive numbers. Function that are a composition may have restricted ranges even if the domain is everywhere.

The size of the domain and range are unrelated. Consider the function f(x) =0. The domain is huge and the range is tiny.
 
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