Let f be a function defined on binary strings as follows:

If u is a string such that u $=$ ab where $|$a$|=|$b$|$ then f$($u$)=$ b$.$

For example, if u $=10110101,$ then f$($u$)=0101.$

Which of the following statements are true?

$*$ fis onto the set of all binary strings.

$*$ The range of fis the set of all binary strings.

$*$ If $|$u$|=24,$ then f$($f$($u$))$ is not defined

$*$ The cardinality of the set $\{$u $|$ f$($u$)=$ u$\}$ is $1.$

$*$ fis a total function.

$*$ Fis an injection.