The discussion revolves around the conditions necessary for the existence of the inverse of a function composition, specifically focusing on the function g^(-1)f. Participants are exploring the relationships between the domains and ranges of the functions involved.
Some participants have provided insights regarding the types of relationships that are considered functions, noting the distinctions between one-to-one and many-to-one relationships. However, there is still exploration regarding the implications of these relationships on the composition fg^(-1).
Participants are discussing the definitions and properties of functions and their inverses, indicating a need for clarity on these foundational concepts. There is a repeated emphasis on the conditions required for function compositions to be valid.
thereddevils said:Homework Statement
What is the condition for the function g^(-1)f to exist ?
Homework Equations
The Attempt at a Solution
i know for function gf to exist , the range of f must be a subset or equal to the domain of g . Does it also work for g^(-1)f ? what is the logic behind that ?
Cilabitaon said:Do you know which types of relationships are considered functions?
thereddevils said:yes , one to one relationships or many to one for functions and one to one only for inverse function
Cilabitaon said:Then there's your answer!