There's nothing terribly complicated going on here. The problem is the abstract set-builder notation. Pick it apart piece by piece.
What type of object does f return, e.g. what type of object is f(1)?
Write out the definition of f with the substitution k=1. Then write a description in words of what's in f(1).
Do your answers for f(1) and f(3) use the right number of curly brackets? What type of object is f(1) or f(3) supposed to be?
Once you understand the function f, try to figure out what's in the set P.
You've already written out part of what's in P, in your answer to part (a). Write out the full contents of P.
Make sure you've answered the question completely. Did you address all three conditions? Did you say explicitly whether P is or isn't a partition?