Inverses, one2one, onto functions

  • #1
StephenPrivitera
363
0
What's an example of a function f(x) such that g(f(x))=x for some g but there is no h such that f(h(x))=x?
I came up with a proof that showed that there is no such function f, but I relied on the fact that a function that is one to one has an inverse. Apparently a function must also be onto. What is the definition of inverse and what guarantees the existence of an inverse such that f(g(x))=g(f(x))=x?
What function is one to one but not onto and does not have an inverse?
 

Answers and Replies

  • #2
theriddler876
98
0
A function is nothing more than a line, but instead of Y you use F of X, it's all pretty stupid if you ask me
 
  • #3
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
What function is one to one but not onto and does not have an inverse?

ex as a function from R to R is a simple one. If f(x) is the inverse to ex, then what is f(-1)?

This also demonstrates a property of 1-1 functions; if you restrict the range, you can make an inverse. In this case, if we view ex as a function from R to R> (the positive reals) then ex does have an inverse; ln x.
 
  • #4
jacksondr
3
0
Inverses

Do all functions have inverses? (If you place restrictions)
Do all graphs have inverses?
 
  • #5
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
Do all functions have inverses? (If you place restrictions)

Trivially yes... I could restrict the domain and range to a single point! (though, usually, you can get useful results without such a harsh restriction) For differentiable functions, you might want to look up the inverse function theorem.


Do all graphs have inverses?

TMK, The term "inverse" doesn't apply to graphs.
 
  • #6
jacksondr
3
0


I asked three other teachers at my high school: Do all functions have inverses? Responses: I don't know, maybe, and no because of problems with complex numbers. I looked up the theorem of inverse functions with regard to derivatives and am satisified with that. So your answer to the questions is yes, if you aren't concerned with restrictions? Thanks
 

Suggested for: Inverses, one2one, onto functions

Replies
17
Views
368
  • Last Post
Replies
6
Views
857
Replies
15
Views
164
  • Last Post
Replies
16
Views
793
MHB Functions
  • Last Post
Replies
2
Views
535
Replies
2
Views
370
  • Last Post
Replies
4
Views
439
Replies
5
Views
468
  • Last Post
Replies
9
Views
1K
Top