Show that if x(t) is even, then so is X(s).

[plexus0208]

Homework Statement

If a signal x(t) is an even function, how do I show that its Laplace transform X(s) must be even as well?

Homework Equations

X(s) = Integral(-inf,inf) of x(t)*e^-st dt

The Attempt at a Solution

I can show this for specific functions x(t), but how would I show this in general? My signals and systems textbook doesn't seem to say anything about even/odd Laplace transforms.

 

[praharmitra]

Write X(-s) as an integral. Then change integration variable from t -> -t. Use the evenness of x(t).