3.47. Show the following properties for the Laplace transform: (a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even. (b) If x() is odd, then X(-s) - - X(); that is, X(s) is also odd. (c) If x(1) is odd, then there is a zero in X(s) at s - 0.

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3.47. Show the following properties for the Laplace transform:
(a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even.
(b) If x(t) is odd, then X(-s)--X(s); that is, X(s) is also odd.
(c) If x() is odd, then there is a zero in X(») at s - 0.
Transcribed Image Text:3.47. Show the following properties for the Laplace transform: (a) If x(1) is even, then X(-s) = X(s); that is, X(s) is also even. (b) If x(t) is odd, then X(-s)--X(s); that is, X(s) is also odd. (c) If x() is odd, then there is a zero in X(») at s - 0.
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