Yes I understood this, but thanks for making sure anyway...
That still does not answer my question. I see and understand the utility of fixed parameter tractability.
This naturally made me wonder about the proofs that a certain problem type P' is NP-hard (by being able to transform problem from P' to known NP-hard problem P and back): can these translations be used to deduce the relevant fixed parameter for NP-hard problems if one of the 2 problem types (P' or P) has a known fixed parameter tractable algorithm...
I.e. you did not answer my question at all, you just reiterated basic complexity theory
That still does not answer my question. I see and understand the utility of fixed parameter tractability.
This naturally made me wonder about the proofs that a certain problem type P' is NP-hard (by being able to transform problem from P' to known NP-hard problem P and back): can these translations be used to deduce the relevant fixed parameter for NP-hard problems if one of the 2 problem types (P' or P) has a known fixed parameter tractable algorithm...
I.e. you did not answer my question at all, you just reiterated basic complexity theory