In this case, I would talk to the dealer you bought it from and tell them they should fix it for free. The hose itself is probably $10 and it would take them probably 20-30 minutes. I would request they do it for free is because hose shouldn't be damaged after only 72 hours. I can't tell exactly what's wrong from the picture, but I would guess it wasn't installed/positioned properly to begin with.. and the dealer is supposed to check all that stuff before delivering it to you. For reference, my 2011 F50 has about 360 hours and that hose isn't frayed at all.
If they don't fix it for free, it's a relatively easy job to do yourself. However, you have to drop the lower unit so you can disconnect that end of the hose. The other end should be reachable without having to remove anything, but dropping the lower unit does require a socket wrench and probably a buddy to help hold it up when you take the bolts off.
If you plan on doing the basic maintenance yourself going forward, then dropping the lower unit is something you'll want to learn how to do anyway. There are plenty of YouTube videos on how to drop the lower unit on Yamahas (just search for something like "yamaha impeller change"). I would just watch a couple and decide if you're comfortable doing it. The worst thing that generally happens when people do it the first time is the shift shaft gets misaligned and it won't go into forward or reverse gear. But that's easily fixed by manually turning the shaft and reinstalling it.
The other thing is, how long can you stand the boat being out of the water? The dealer might agree to fix it for free, but you might be 30th in line as far as other jobs they're working on.. so it might take a few weeks before you get it back.