1)-why is x(t)+x(-t) always even??..no matter if x(t) even or odd??? 2)-when we talk about unit step function...u(t)..and we add..u(t)+u(-t)..the value of both is 1 at t=0..so does'n't that gets added twice??..and it becomes 2 at t=0... 3)when we have x(-t) and we time shift it say x(-t-3) it shifts toward the -ve t axis.. where as x(t-3) the function is shifted on the + axis..why is it so?? i would be really greatful if you can help me out with the above 3 doubts..