[help] Fourier Optics problem

question2004

Suppose that a sinusoidal input g(x,y)=cos[2*pi(x*fx+y*fy)] is applied to a linear system. Under what (sufficient) conditions is the output a real sinusoidal function of the same spatial frequency as the input? Express the amplitude and phase of that output in terms of an appropriate characteristic of the system

From Goodman Introduction to Fourier Optics 2nd ED

I have no idea of how to do it. Thanks a lot