Let A and B be two sets different from the empty set. A correspondence assigning each element of the set A, one and only one element of the set B is called a function from the set A into the set B. Functions are generally denoted by the lower case letters such as f, g, h. In this case a function defined from the set A to the set B is denoted by

                                    f:  or . 

In this context, the set A is called the domain or the departure set of the function, and the set B is called the range or terminal set. For a given function f and an element a from its domain A, the element corresponding to a under the rule f  is called the image of the element a, and is denoted by f (a).

As also understood from the information given, all of the statements regarding to functions in the options are correct, so the correct answer is E.