The impulse response h (t) of a LTI system is given by h (t) = exp (-2t) u (t) where, u (t) denotes the unit step function. The output of this system to the sinusoidal input x(t) = 2 cos(2t) for all t, is _____________

(a) 0

(b) 2^-0.25 cos(2t-0.125π)

(c) 2^-0.5 cos(2t-0.125π)

(d) 2^-0.5 cos(2t-0.25π)

I had been asked this question during an online exam.

My question is taken from Region of Convergence topic in chapter Laplace Transform and System Design of Signals and Systems