When Can We Find the Inverse of a Function Composition?

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For the function g^(-1)f to exist, the range of f must be a subset of the domain of g^(-1). This is similar to the condition for gf, where the range of f must align with the domain of g. Inverse functions require a one-to-one relationship, which is crucial for g^(-1) to be defined. The discussion also touches on the differences when considering fg^(-1), indicating that the relationships between the functions must still adhere to these domain and range conditions. Understanding these relationships is essential for determining the existence of function compositions and their inverses.
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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 ?
 
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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 ?

Do you know which types of relationships are considered functions?
 


Cilabitaon said:
Do you know which types of relationships are considered functions?

yes , one to one relationships or many to one for functions and one to one only for inverse function
 


thereddevils said:
yes , one to one relationships or many to one for functions and one to one only for inverse function

Then there's your answer!
 


Cilabitaon said:
Then there's your answer!

thanks ! How is it different when its fg^(-1) ?
 

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