(Properties of Continuous Systems) Determine (with justification) whether the follow- ing systems are (i) memoryless, (ii) causal, (iii) invertible, (iv) stable, and (v) time invariant. For invertibility, either find an inverse system or an example of two inputs that lead to the same output. Note that y(t) denotes the system output and z(t) is the system input.
a) y(t) = (t - 2)2(t+2)
b) y(t) = 2(t-1) + x(4- t)
c) y(t) = x(sin(t))
d) (Optional, not graded) y(t) = { 0, So r(t – T)dt, z(t) <1, r(t) > 1.