How do I view the list of functions a Linux shared library is exporting?

Question

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.

objdump -T *.so may also do the job

On a MAC, you need to use nm *.o | c++filt, as there is no -C option in nm.

Among other already mentioned tools you can use also readelf (manual). It is similar to objdump but goes more into detail. See this for the difference explanation.

$ readelf -sW /lib/liblzma.so.5 |head -n10

Symbol table '.dynsym' contains 128 entries:
   Num:    Value  Size Type    Bind   Vis      Ndx Name
     0: 00000000     0 NOTYPE  LOCAL  DEFAULT  UND
     1: 00000000     0 FUNC    GLOBAL DEFAULT  UND pthread_mutex_unlock@GLIBC_2.0 (4)
     2: 00000000     0 FUNC    GLOBAL DEFAULT  UND pthread_mutex_destroy@GLIBC_2.0 (4)
     3: 00000000     0 NOTYPE  WEAK   DEFAULT  UND _ITM_deregisterTMCloneTable
     4: 00000000     0 FUNC    GLOBAL DEFAULT  UND memmove@GLIBC_2.0 (5)
     5: 00000000     0 FUNC    GLOBAL DEFAULT  UND free@GLIBC_2.0 (5)
     6: 00000000     0 FUNC    GLOBAL DEFAULT  UND memcpy@GLIBC_2.0 (5)