Hmmm ... seems like some of the choices of operators and regular expresssions are somewhat arbitrary. Did you guess :) ? Couple of hints:
The operator to match a string with regular expression is =~, not .=
Capturing a single dot in parentheses ((.)) doesn't really make sense unless you want to capture the very character this dot matches and save it in a variable.
To match either f or g, use a character class: [fg]
Remains the question where you've got those ideas from ...