> the function in question is not given any inputs
As the problem was posed, the function does take an input; it's defined as a function from {0, 1} to {0, 1}. However, as I pointed out in another comment upthread, the function makes no use of its input so it could just as well be defined with no inputs. (Indeed, even if you read the question as asking about a function f that outputs 1 if God exists or 0 if God doesn't exist, it doesn't seem like whether or not God exists is supposed to be an input.)
As the problem was posed, the function does take an input; it's defined as a function from {0, 1} to {0, 1}. However, as I pointed out in another comment upthread, the function makes no use of its input so it could just as well be defined with no inputs. (Indeed, even if you read the question as asking about a function f that outputs 1 if God exists or 0 if God doesn't exist, it doesn't seem like whether or not God exists is supposed to be an input.)