Welp... My front derailleur shifter cable snapped where it attaches to the front derailleur... I bough the bike about 3 weeks ago from performance bike... My question is, will they replace it for me? Installation and everything? I don't mind buying the cable but saving a few bucks would be fine as well...

They are a phone call away.

Yep, they should replace that for you. Breaking at that point in 3 weeks is bad cable or bad installation. Talk to them. This is assuming the shop is local to you. If not, they should send you a cable.

A cable that breaks in only 3 weeks isn't normal. It should be looked at to see where, and why it broke. Sounds as if it wasn't attached properly to the derailleur

Sounds like whoever assembled it overtightened the bolt that holds the cable. Tighten that bolt too much and I guess you could crush the cable to the point where it's strength is compromised.

Or derailleur stops were too tight.

FIFY. This strikes me as one of the JRA stories.

Just to be the devil's advocate...

Faulty installation is the most likely cause, in my opinion. Regardless of the cause, if I was in the shop, I'd be happy to replace a cable on a 3-week-old bike as a goodwill gesture since it's cheap & easy.

Since the OP would not have installed the cable on a new bike(it would have been done in the factory) I would think that the shop should darn well replace it free of chanrge

Agreed. I just phrased it that way in response to Looigi's suggestion that the customer could somehow be at fault. Whether it's faulty installation as we suspect or customer misuse/abuse, it's a cheap and easy fix and the shop should take care of it.