Can you go back to the previous iOS version after updating?

Only for a short window. Apple keeps signing the previous version for a week or two after a release, and once it stops you can't put it back on the phone at all, whatever tool you try. While it's still signed you download the ipsw for your exact model, plug into a mac or itunes, and option-click (shift-click on windows) Restore. The catch is the backup: one made on the newer ios won't restore onto the older one, so you'd be setting up fresh or from an older backup. If you're on a beta it's easier - delete the beta profile and wait for the next public release.