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and I need to find the range for the function.

So I proceed to find the inverse [ ( e^(2x) - e ) / 2 ] ^ (1/3) = y

my memory is a little sketchy but don't I need to put the domain boundary value for the original into the inverse to find the range (apparently not because my graphing calc shows otherwise). -- If not does that mean the range of the original function is all real numbers?