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Hi,
sage is correct saying that a negative number cannot be raised to a fractional power IF you want to plot it. For example
f(-2)=-1/2*sqrt(-2)
f(2)=sqrt(2)
The first one is imaginary, the other one real, so you cannot plot both in the same 2D plot. You could use the abs() function to avoid this problem. Another thing is
sage: f(x).limit(x=0,dir='+')
0
sage: f(x).limit(x=0,dir='-')
+Infinity
so that your plot for either f or g will have a huge peak which will suppress the rest of the plot. Try the following:
sage: f1(x)=x^(1/x)
sage: f2(x)=(-x)^(1/x)
sage: p1=plot(f1(x),0,5)
sage: p2=plot(f2(x),-5,-0.5)
sage: show(p1+p2)
