The correct command to extract the contents of the compressed archive file1.tar.gz is tar -xzf file1.tar.gz. This command uses the following options:

-x means extract files from an archive.

-z means filter the archive through gzip, which is a compression program that reduces the size of files.

-f means use the following archive file name, which is file1.tar.gz in this case.

The other commands are incorrect for the following reasons:

tar -czf file1.tar.gz creates a compressed archive file1.tar.gz from the files specified after the command, not extract it.

ztar file1.tar.gz is not a valid command, as ztar is not a standard program or option for tar.

tar --extract file1.tar.gz is missing the -z option to handle the gzip compression, and also the -f option to specify the file name.

detar file1.tar.gz is not a valid command, as detar is not a standard program or option for tar.

References:

Linux Essentials - Topic 106: The Linux Operating System, section 106.2 Use single shell commands and one line command sequences to perform basic tasks on the command line.

LPI Linux Essentials Study Guide: Exam 010 v1.6, 3rd Edition, Chapter 5: Working with Files and Directories, section Compressing and Archiving Files.