Let $j:U\rightarrow X$ an open immersion between kschemes of finite type and $f:X\rightarrow S$ a surjective kmorphism of finite type.
We suppose that $f\circ j:U\rightarrow S$ is faithfully flat, does it imply that f is faithfully flat?
Let $j:U\rightarrow X$ an open immersion between kschemes of finite type and $f:X\rightarrow S$ a surjective kmorphism of finite type. We suppose that $f\circ j:U\rightarrow S$ is faithfully flat, does it imply that f is faithfully flat? 

