give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist. explain your answer.

Answer 1

(hog)(x) = h(g(x))

let g(x) = x or just about anything

and let h(x) = 1/x(0)

h(g(x)) = 1/x(0) = 1/0 which is undefined

at least it has no real solution. It does have "surreal" solutions, infinity or -infinity, but they are not real numbers. They have a "surreal" existence.