I built a house and included an area that I use exclusively for business. Can I deduct the cost of building that part of the home for the office?

Yes, you can depreciate that part of the home that you use for business. You cannot claim a deduction for full cost of constructing that area of your home but the can depreciate it over a period of 39 years. Please read Publication 587 and read the section entitled Depreciating Your Home.