Question

True or False: The domain of an inverse of a relation is the domain of the original relation.

Answer 1

False, you're welcome :)

Answer 2

 False. 

An example of where  it is false is f(x) = x^2 {domain is all reals}. The inverse f^-1(x) = sqrt(x) has a domain of all reals greater than or equal to zero.
hope this helps