Are f(x)=x1/3f(x) = x^{1/3}f(x)=x1/3 and g(x)=x3g(x) = x^3g(x)=x3 inverse functions?
No
f′≠1/g′f' \ne 1/g'f′=1/g′
Yes, compositions equal xxx
Only on (0,∞)(0,\infty)(0,∞)