Let f Qlx]. Let f'(x)=x^d*f(1/x) where d=deg f > 0. Show that f' Q[x], and that assuming x does not divide f, we have that f is irreducible in Q{x] if and only if f' is irreducible in Q[x]

f ' = x^d f(1/f) where d = degree of f >0

looking to show that the polynomial f in Q[x} is irreducible if and only if f ' in irreducible in Q[x}