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For an energy signal g(t) with energy Eg, show that the energy of any one of the signals -g(t), g(-t) and g(t-T) is Eg. Show that the energy of g(at) is Eg/a.

While I can arrive at the answers intuitively, the total area under the curve is constant for the first parts and is being reduced or increased for the second part, I cant figure out how to mathematically prove any of these except the case of -g(t). I am starting with the basic definition of the energy signal Eg=integral(g(t)^2,t,-inf,inf) but I cant figure out a way to get any further without an actual function.Can anyone give me any guidance?

Thanks so much.