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?

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

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

c$)f$ is a total function.

d$)f$ is onto the set of all binary strings.

e$)F$ is an injection.

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