I'm going to try my best, but since I'm not too familiar with these questions, it might be wrong.
I'm going to follow the hint, and assume that f(x) is a periodic function of period T and try to prove that this equation is impossible.
f(x + T) = f(x)
pi*(x + T)^2 - cos(x + T) = pi*(x)^2 - cos(x)
pi*x^2 + 2*pi*xT + pi*T^2 - cos(x + T) = pi*(x)^2 - cos(x)
2*pi*xT + pi*T^2 - cos(x + T) = - cos(x)
2*pi*T(x + T) + cos(x) = cos(x + T)
2*pi*T(x + T) + cos(x) = cos(x) * cos(T) - sine(x) * sine(T)
And... now I'm stuck. :((
Maybe someone else can give help?
I'm really sorry that I wasn't able to help more.
=^._.^=