The new set, [tex] f(a) [/tex], is a set consisting of all [tex] x \epsilon A [/tex] s.t. [tex] x \leq a [/tex].
For example, consider [tex] A = \mathbb{N} [/tex]. Look at [tex] f(5) [/tex]. This is simply [tex] \{1,2,3,4,5\} [/tex].
So, for the first part, you need to show that
[tex] f(a)=f(b) \Rightarrow a=b [/tex]
I'll stop here, just in case you need more assistance.
