Question

which statement could be used to explain why tge function h(x)=x^3 has an inverse relation that is also function

Answer 1

The function x^3 is a one-on-one function. 
This means that for every element of the range of the function corresponds to exactly one element of the domain.
This means the inverse function (which is whiching the range and the domain) will also be one-on-one function.