PostgreSql function slows down view
As an answer,


  What exactly does the function do? Can you define it as stable or even better as immutable? – a_horse_with_no_name 12 mins ago


From the docs


  IMMUTABLE / STABLE / VOLATILE These attributes inform the query optimizer
  about the behavior of the function. At most one choice can be
  specified. If none of these appear, VOLATILE is the default
  assumption.
  
  
  IMMUTABLE indicates that the function cannot modify the database and
  always returns the same result when given the same argument values;
  that is, it does not do database lookups or otherwise use information
  not directly present in its argument list. If this option is given,
  any call of the function with all-constant arguments can be
  immediately replaced with the function value.
  STABLE indicates that the function cannot modify the database, and
  that within a single table scan it will consistently return the same
  result for the same argument values, but that its result could change
  across SQL statements. This is the appropriate selection for functions
  whose results depend on database lookups, parameter variables (such as
  the current time zone), etc. (It is inappropriate for AFTER triggers
  that wish to query rows modified by the current command.) Also note
  that the current_timestamp family of functions qualify as stable,
  since their values do not change within a transaction.
  VOLATILE indicates that the function value can change even within a
  single table scan, so no optimizations can be made. Relatively few
  database functions are volatile in this sense; some examples are
  random(), currval(), timeofday(). But note that any function that has
  side-effects must be classified volatile, even if its result is quite
  predictable, to prevent calls from being optimized away; an example is
  setval().
  
  
  For additional details see Section 36.6


The real question is essentially, can you optimize away f(x)


Over everything (mathematical purity)
Over the same scan
Never (uses IO or system calls)


A somewhat important note is that even in production applications you can sometimes lie and say IMMUTABLE and it's perfectly fine. Just be aware of the consequences.