Preimage of SHA512 with a known suffix Is it possible to figure out what $arg1 is if I know both $arg2 and $arg3 in addition to $hash?

$hash = hash('sha512', $arg1 . $arg2 . $arg3);
Assuming that . represents concatenation, no, except in the specific case that $arg1 is the empty string.  You're trying to perform a preimage attack, which is one of the things that SHA512 is designed to be resistant to.

Further, knowing $arg2 and $arg3 does not let you speed up a brute-force attack on $arg1, because for each candidate value for $arg1, $arg2 and $arg3 will modify the checksum differently.  (If you knew $arg1 and $arg2 and were looking for $arg3, you could precompute the partial checksum of the first two values as the starting point for each try at finding $arg3)