Proving Irreducibility of Polynomials in Fields

[playa007]

Homework Statement

Let k be a field, and let f(x) = a_0 + a_1x +a_2x^2 +...+a_nx^n in k[x] having degree n. If f(x) is irreducible, then so is a_n + a_n-1x+...+a_0x^n

Homework Equations

The Attempt at a Solution

A function that "reverses" the coefficients is not a well-defined function so it is necessary to use another approach. I'm wondering how this can be done, I'm pretty sure Eisenstein's Criterion isn't of much use here.

Any help would be highly appreciated.

 

[epenguin]

A function that "reverses" the coefficients is not a well-defined function

?
Is it any help that your second function is f(y)/y^n where y = 1/x ?