Questions about F5 BIG-IP Multi-Datacenter Configuration

what kind of route injection do you use?
is it LTM virtual address Route health injection like in this article?
https://my.f5.com/manage/s/article/K15923612

DNS client dont have mechanism to check whether dns server is healthy or not before sending request,
so it will only know unavailability based on timeout.

for servers/apps accessed using hostnames, implementing F5 DNS/GTM will be better than RHI.
you can use the cheap F5 DNS VE version, 1 in each DC, because DNS traffic is very small.