Two mappings with constant composition Can you tell me if my answer is correct? Thank you so much!!!
Here is the problem:
If $f,g$ are mappings of $S$ into $S$ and $f\circ g$ is a constant function, then
(a) What can you say about $f$ if $g$ is onto?
(b) What can you say about $g$ if $f$ is 1-1.
Original Image
As $f\circ g$ is a constant function, $f\circ g$ is neither onto nor 1-1.
If $g$ is onto, $f$ cannot be onto because if $f$ is onto and $g$ is onto, $f\circ g$ would be onto.
If $f$ is $1-1$, $g$ cannot be 1-1 because if $f$ is 1-1 and $g$ is 1-1, $f\circ g$ would be 1-1.
In any case, the range of $g$ must be a subset of the domain of $f$.

Hints/Solutions:
(a) $f$ is constant.
(b) $g$ is constant.
