The given statement is,
If f is a function defined on the domain of all real numbers and has an inverse, then the inverse of f is defined on the domain of all real numbers.
Which is a true statement.
By the definition, a true inverse can only exist if a function is one-to-one.
In the one-one function, we can see that if the domain of f is from negative infinity to infinity (i.e. real numbers) then the range of F is negative infinity to infinity (i.e. real numbers).
Since the domain and range of the function are the same, both the function and its inverse will have the same domain.
So, the given statement is a true statement.