Question 1186928
.
For each of the following statements, explain why it is true for all functions f and g or an example of specific functions f and g showing that it is false.

a. All elements in the domain of g must be in the domain of f o g (fog)
b. All elements in the range of f must be in the range of f o g
~~~~~~~~~~~~~~~~~~~~~



In the post by  @CPhill  (Artificial  Intelligence  ?),   the answer  " True "  in part  (a)  is a   {{{highlight(highlight(FATAL))}}}   {{{highlight(highlight(ERROR))}}}.



Counter-example:    g(x) = x;   f(x) = {{{1/x}}}.


Then  x = 0   is in the domain of  g,   but is  NOT  in the domain of   (fog)(x) = {{{1/x}}}.



By the way, it means that all the argumentation of @CPhill in part  (a)  is invalid,
although it produces quite solid impression.



A stern examiner would give a solid  " {{{highlight(highlight(2))}}} "  to such an  " artificial intelligence "  student.



But remember,  that an  " artificial intelligence"  claims not to be  " a student ", 

but to be a  " SUPERIOR  MIND ",  who does not make mistakes,  knows everything 

and leads everybody around to a bright future  ( ! )



What I want to say is that still there are plenty of the room to improve your skills

as an "artificial intelligence" before you become a true "Artificial Intelligence".