Apply every function from a list to an expression

I would like to apply a list of functions to an expression, like

ApplyList[{Re, Im}, Exp[I x]] = {Cos[x], Sin[x]}

How do I do that?

Answer

thru1 = Assuming[Element[x, Reals], Simplify @ Through @ {Re, Im} @ ComplexExpand@#]&;

thru1 @ Exp[ I x]
(* {Cos[x], Sin[x]} *)

Or

thru2 = Composition[Assuming[Element[x, Reals], Simplify@#] &, 
                   Through@{Re, Im}@# &, ComplexExpand];


thru2 @ Exp[I x]
(* {Cos[x], Sin[x]} *)

Or

thru3 = Fold[#2[#] &, Exp[I x], 
     {ComplexExpand, Through@{Re, Im}@# &, Assuming[Element[x, Reals], Simplify@#] &}];

thru3 @ Exp[I x]
(* {Cos[x], Sin[x]} *)