Proving Energy of a Signal: g(t)

[Infidel22]

Hi, I am having a bit of a problem regarding a simple proof for a generic energy signal, the question reads as thus:
For an energy signal g(t) with energy Eg, show that the energy of anyone 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 can't 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 can't figure out a way to get any further without an actual function.Can anyone give me any guidance?

Thanks so much.

 

[Galileo]

For all the other ones, you should use an appropriate change of variables. Look at the definition of Eg for the specific g given and think about what a good choice for a change of variable would be.