Question

Let f:A->B and g:B->c be functions.
Give an example of functions f and g such that g is not one to one but f is one to one and g of f is one to one.

Answer 1

hmm lets try this and see if it works

Answer 2

put
\[g(x)=\sin(x)\] a many to one function and
\[f(x)=\sin^{-1}(x)\] a one to one function. then
\[g\circ f(x)=\sin(\sin^{-1}(x))=x\] a one to one function

Answer 3

looks ok to me

Answer 4

The question was asked in the context of transformations, so I believe when it asks f: A->B it is the function that maps the coordinate in set A to set B, so it's a bit different from, say, the trig function you used as an example. idk.