Use solve command to determine a shift value for graph?

Questions
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1

Hello,

I have created a code for my graph: Manipulate[Plot[E^-2 x Cos[Pi x] + c, {x, -3, 4}], {c, 0, 3}]
Using the sliders, it appears that F[x] must be shifted up approximately 2.12341 units up in order to pass through the point (1,2).
However, I would like to know how to use the solve command to determine what the exact shift value is for the graph to pass through (1,2).
I have already tried looking up the Mathematica solve command, but I could only find articles for other equations and none that could help me in this case.

Thank you.

Screen Shot 2018-10-11 at 2.06.54 PM.png
Screen Shot 2018-10-11 at 2.06.54 PM.png1416×792 42.2 KB

2

for x=1 function should be equal to 2.

   eq = E^-2 x Cos[Pi x] + c == 2;
   sol = Solve[eq /. x -> 1, c]
   (* {{c -> (1 + 2 E^2)/E^2}} *)
   %//N
   (* {{c -> 2.13534}} *)

   (eq /. x -> 1) /. sol
   (* {True} *)
3

Mariusz, I really really appreciate you and your help as always… very kind of you.

Thanks again.