Troubles with BlankNullSequence in the case of multiplication

Question

I have some trouble to use the triple underscore notation to use definitions with or without a term. Consider the following toy example

f[a___ x]:=1
{f[x],f[2x]}

This returns

{f[x],1}

whereas I would like the $f[x]$ pattern to be matched. I guess it is not recognizing "1" as an empty element. How can I arrange this definition to get {1,1} as an output ?

Answer 1

f[a_. x] := 1
{f[x], f[2 x]}

---

{1, 1}