I'm new here, though I wish I had found this forum long ago. (I'm an applied math major.)
I've run into trouble on my homework which is, of course, due tomorrow. Here we go:
If f: A -> B and g: B -> C are one-to-one functions, show that (g o f)^-1 = f^-1 o g^-1 on Range (g o f).
I'm stuck on where to even start on this proof, and it's driving me mad. For the record, the above notation ^-1 denotes "inverse". Please help?
I'm not sure I'm on the same page with you here with the above. Let me see if I can use this math code to produce what I'm saying, because I feel like I'm not quite getting it still.
Okay, that's what I'm supposed to prove. Do I still do the same as above, or does the strategy change?
It's and . Or, I suppose if you prefer, and .
You'll have to pardon me if I sound rather confused (well, I am, forgive me!). I've spent the past hour or so at least on this problem, and proofs have never been anything near my strong point.
Crud, I'm sorry! I mixed up the latter equation!
I'm such an idiot, I'm sorry! That's what I'm supposed to prove.