f(x)=(x+100)3 is an example of a one-to-one function (for every x there is one and only one y=f(x)). The domain is from -∞ to ∞, as is the range.
x+100=∛y where y=f(x), so x=(∛y)-100. If x=g(y) then g(y)=(∛y)-100, and g(x)=(∛x)-100. g(x)=f-1(x), the inverse of f.