Is the Inverse of a One-to-One Odd Function Also Odd?

[n-000]

Hello all

Thses are my questions:


1. Prove that if A(x) is a one to one odd function, then A^(-1) (x) is also odd function.





2. If D(x) and R(x) are one to one functions, then
(DoR)^(-1) (x)=(R^(-1) o D^(-1) )(x)


I hope that someone will help me ^^

 

[Mark44]

You have to make an effort at proving these before anyone can give you any help.

 

[n-000]

Actually, in general I want to know how to prove any question?

 

[snshusat161]

How to prove any question? You have asked very difficult question. I think the best way is to experience it by looking at examples and solving problems, at least trying to solve.
Some commonly used way to prove are

(i)Solve L.H.S and the R.H.S, if both give same result then it is proved
(ii) Solve either of L.H.S or R.H.S to prove other side.

(iii) Prove it by making some contradiction

 

[snshusat161]

How to prove any question? You have asked very difficult question. I think the best way is to experience it by looking at examples and solving problems, at least trying to solve.
Some commonly used way to prove are

(i)Solve L.H.S and the R.H.S, if both give same result then it is proved
(ii) Solve either of L.H.S or R.H.S to prove other side.

(iii) Prove it by making some contradiction

 

[PhaseShifter]

Start by defining the terms used, writing them as equations if possible.

What does it mean to say "A(x) is one to one"?
What does it mean to say "A(x) is an odd function"?
What is the definition of A^(-1) (x)?

 

[n-000]

Thank you all
Your advices were very helpful ^^