When Can We Find the Inverse of a Function Composition?

  • Thread starter Thread starter thereddevils
  • Start date Start date
AI Thread Summary
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.
thereddevils
Messages
436
Reaction score
0

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 ?
 
Physics news on Phys.org


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) ?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Composite and Inverse Functions Problem
Replies
3
Views
2K
Finding the domain of a composite function
Replies
10
Views
2K
To find the range of a given ##\sin## function
Replies
15
Views
2K
Spivak chapter 3 problem 24 - proof of a composition
Replies
2
Views
2K
What is the range of the composite function h?
Replies
4
Views
2K
Domain and Range of a Function and Its Inverse- Polynomials
Replies
9
Views
2K
Counter example to: if f*g is inv then f & g are inv
Replies
2
Views
2K
How does this composite function simplify to 2(2^x) ?
Replies
3
Views
2K
State the domain and range for a given function
Replies
7
Views
2K
Curiosity about why this is not a Function composition
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top