Composite Functions: Inverse of f o g?

[Monsu]

If f:A -> B and g:B -> C are functions, is this true: f o g is also a function and (f o g) ^-1 = gof

I think this isn't true, but if this isn't the case, could someone please tell me a counter example?? Thanks

 

[matt grime]

with that notation fog is not a function, gof is a function from A (to B thence) to C. but that is just the notational convention: functions read from right ot left. the inverse part *is* wrong. firstly that isn't function, never mind one that posses an inverse (which a function) may or may not do. So it's hard to find a counter example given that.

 

[Monsu]

Thanks, but what could be a counterexample for it??

 

[matt grime]

erm, counter example to what? g sends an element of B to an element in C, right? You cannot then follow that with a function from A to anywhere since C is not necessarily a subset of A. counter example is any function g where its image does not lie in the domain of f.

this looks a lot like homework, so i think you should be able to find a counter example if you want to; I've given you the reason why it is not necessairly true