Give an example of a pair of functions f: B onto C and g: A onto B such that f(g(x)): A onto C is ........?

one to one but f is not one to one?

Give an example of a pair of functions f: B onto C and g: A onto B such that f(g(x)): A onto C is ........?
An even simpler example: Let A = C = {1, 2, 3} and B = {1, 2, 3, 4}. Then let f be the identity map and g be the identity map on 1, 2, 3, and g(4) = 3.
Reply:f =x^2


g= sqrt(x)





f(g(x))=x





f(g(x)) is one to one but f is not .

funeral flowers