How about ?Let P be a polynomial of degree n.
1.) Can P have an inverse if n is even. Support your answer.
2.) Can P have an inverse if n is odd? If so, give an example. Then give an example of a polynomial of odd degree that does not have an inverse.
For 1.) I think that no P's can have an inverse if they are even because they would fail the HLT.
For 2.) I'd say yes P can have an inverse if n is odd such as the inverse of f(x) = x^3 is f^-1(x) = x^(1/3).
I cannot think of an example of a polynomial of od degree that does not have an inverse though. Please help