The swap object reverses the order of the inlets: left inlet goes to right outlet and right inlet goes to left outlet.
On the left side we show a swap object with two numbers on the inlets, which are reversed in the outlets. You have to connect the cold inlet (right inlet) first to the bang. The better method will be to have a trigger object, so you can tell order of connections just by looking.
On the right side, instead of using right inlet, we use 1, so 1 will always be on left outlet. Here, we are implementing 1/x, where x is the input into left inlet of swap 1.