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I'm struggling with the following code

f[x_] := {Undefined, x};
Plot[ f[x] , {x, 0, 1}]                    
Plot[{f[x][[1]], f[x][[2]]}, {x, 0, 1}]
f[x] == {f[x][[1]], f[x][[2]]}

The first plot produce blank figure and the second plot gives the graph of x as expected. What is puzzling, the last condition evaluates to True.

Can you please explain to me why the first plot gives blank plot while the second does not?

tom
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