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?

$F$ is an injection.

$f$ is a total function.

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

The range of $f$ is the set of all binary strings.

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

$f$ is onto the set of all binary strings