Can someone do a proof of why f(f^-1(x))=x? I attempted it but here is what i got.
Let (x,y) be a coordinate on f(x) and hence (y,x) be a coordinate on f^-1(x)
Thus f(f-1(y))= f(x)=y. Hence the composite function lies on (y,y) for y elemtn of Real.hence y=x
Is my proof correct?
Hi, sorry for the late response. I'll give it a go
Your proof looks to be good, I might give it a little more detail though
Let (x,y) be a coordinate on f(x) and hence (y,x) be a coordinate on f^-1(x)
Therefore f-1(y)=x
Therefore f(f-1(y))=f(x)=y
Therefore the point (y,y) lies on the composite function, therefore the composite function lies on the line y=x therefore f(f-1(x))=x
Sorry if the notation isn't perfect, but your proof should be good