If JavaScript has first-class functions, why doesn’t calling this function in a variable work?

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When you call obj.method() in Javascript the method is passed obj as this. Calling document.getElementById('x') with therefore set this to document.

However if you just write f = document.getElementById you now have a new reference to the function, but that reference is no longer “bound” to document.

So your code doesn’t work because when you call f as a bare function name it ends up bound to the global object (window). As soon as the innards of the function try to use this it finds that it now has a window instead of a document and unsurprisingly it doesn’t like it.

You can make f work if you call it so:

var x = f.call(document, 'x');

which calls f but explicitly sets the context to document.

The others way to fix this is to use Function.bind() which is available in ES5 and above:

var f = document.getElementById.bind(document);

and is really just a generalised short cut for creating your own wrapper that correctly sets the context:

function f(id) {
    return document.getElementById(id);
}

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