What would you play in this position?

White to move, your bishop is under attack, what do you play?

 Quick glance: without a doubt Bg3 (lightning quick reflexes, although I should probably slow down sometimes  ). If Black carelessly plays ...Nxg3 then I play hxg3. I will probably not castle short (O-O), but I now have a nice open h-file for my Rook. If my opponent castles into my potentially powerful h-file (via ...O-O) then I may even consider (if the position allows) getting my light-squared Bishop out, King to e2 and later on even maybe piling on both Rooks on the h-file. Maybe I may setup O-O-O to get my Rooks on the h-file instead. Of course, I would always be careful not to commit myself too deeply until I know my opponent will not ...O-O-O as it would be a tad embarrassing to have my Rooks doubled on the "wrong" side of the board XD.

would you play that to open the rook file? or do you capture back with the other pawn

Yup  answered as I typed. 5.Bg3 is really the only move here. My anticipated Rook idea is a bit more debated and depends on if the position allows.

I understand the trade of Knight and Bishop feeling almost inevitable, but this approach of seeing them as equal is a superficial assessment. White does not want ...Nxf4 and exf4. Why would White willingly give up a valued central pawn (e-pawn) for nothing really. Not all pawns are worth the same and not all pieces are worth the same! Placement/activity can make all of the difference. A central pawn with central influence has a bit more value than a less influencial pawn (like a flank pawn). Clearly, chess offers many exceptions to many rules, and position dictates pretty much all, but here is one of those times not to disrupt "general chess principles." 

I can see why you may want to use a tempo to do something else if the "even" trade is coming anyway, but this exchange on f4 is far from even; Black would be very happy with this setup after an "even" (not really) exchange on f4. IMBacon has a much more pleasing approach for White, with flexibility and does not commit structural/positional suicide. Your "free tempo" idea is correct IF AND ONLY IF the exchange is equal for both sides: unfortunately, for White it is far from equal.

myratingisreally1523, is there something you care to explain that may justify an exchange on f4? Maybe I am missing some tactical idea, or the exf4 somehow realigning itself on the e-file later or something? Allowing this exchange looks absolutely horrid to me at every turn structurally/positionally. 

Even if there is some grand scheme to justify this idea, I would not default to this idea; perhaps after long thought on the position/calculation I may see creative solutions, but I don't understand this f4 exchange for White. Chess aside, we should evaluate rhetoric and our "Target Audience"; the original poster is rated, like me, at a relatively "learning stage" - Bg3 looks far more natural. 

I am by no means backing down yet from my observation that the f4 exchange seems terrible for White? Could you please explain why you hold your belief myrealratingis1523?

I suppose every position has pros and cons if you look for them; I just have trouble allowing the f4 exchange if I was White. It goes against my very being and grain to my logic/way of thinking. Like I said, the natural 5.Bg3 I would play without a second thought and I sense that this move feels far more natural to most chess players too. Thank you for attempting to justify your choice myrealratingis1523, I suppose it takes all kinds of chess players to make a world.  It would be boring if we all defaulted to the same moves/play-styles.

why is this on general chess discussion