you can also see brown - yellow spots at the edges..

Are you watering it with tap water? That would be my best guess as to why this is happening. Dracaenas are particularly sensitive to the fluoride and/or chlorine that is in most tap water supplies. Your best bet would be to use alternate sources, such as rainwater, distilled water, or reverse osmosis water. My preference is for rainwater, because it's basically free.

We don't have fluoride in water. It doesn't rain a lot where I live so rainwater is kind of hard to gather. I use tap water but I usually let it sit for 24-48 hours. I haven't watered it since I got it.. Do you thing this could be from overwatering? Because the pot it came with was dripping when i got it..

If you're watering with tap water, most likely there is fluoride in your water. Cities add it to their water supply for the same reason fluoride is in your toothpaste (to strengthen your teeth). Leaving it out for 24-48 hours only dissipates chlorine. Fluoride won't be removed that way. I filter my water with a PUR water filter, but even PUR states on their website that they don't remove fluoride because it's considered a benefical "ingredient" to water.

Planto

Since you've only had it a week, I don't believe you're responsible for any issues. It is still suffering from its poor treatment in the shop.

I have lived a number of places where the municipal water source has neither fluoride or chlorine. Deep ground water needn't be chlorinated. In any case, I've also had the exact same plant where the water was floridated and chlorinated, and apart from being infuriatingly slow-growing, it never developed any problems.

Slow-growing plants are often also slow-reacting plants because all the biological processes are slowed down.

If it were my plant, I'd gently wash away all the soil and nasties left on the roots from the store. I'd check the bare roots for health, and I'd remove the ones that weren't white, and I would spread out the remaining roots in a nice pot of brand new, healthy soil, amended with at least 50% perlite, pumice, or something to reduce water storage, or I'd plant it in gritty mix. Water sparingly, place in bright light, and keep out of any direct sun for a couple of months to allow it to recover from its previous abuse.

This particular Draceana, in my experience, is very slow, so it might take a while to come around, but I don't think my treatment would make it worse. It think it would only get worse if you find there aren't enough healthy roots to feed the existing foliage.

Just my opinion.

Agree with kwie, Janet Craigs are very very slow! They don't need much water either, so it's not a big deal to give them a drink of bottled water every now and then.
When you cut off the brown part of the leaf, make sure not to cut in green tissue, only the crisp area.
They do well in hydroponics, mine has grown a lot since I transplanted her. She is almost 3 years old. Don't have any brown tips, only on old bottom leaves from the past.
Yours need a repot to some better draining media. If nothing else at hand, you can use cacti and succulent bagged mix and add 50/50 perlite to it.
Wipe the leaves with soft damp cloth or occassionally give her a shower to remove dust.
They don't really need fertilizer.

Ok, that's what I will do.. I hope it will fix the problem.. Thanks again for the help :-)