What you need is nm and
its -D option:
$ nm -D /usr/lib/libopenal.so.1
.
.
.
00012ea0 T alcSetThreadContext
000140f0 T alcSuspendContext
U atanf
U calloc
.
.
.
Exported sumbols are indicated by a T.
Required symbols that must be loaded from other shared objects have a U.
Note that the symbol table does not include just functions, but exported variables as well.
See the nm manual
page for more information.