Only the half you inherited would be valued at FMV at the time of her death. The cost basis in the other half would be determined by when you became the joint owner.
If you were joint tenants with your mother from the time the house was purchased, then 1/2 of your cost basis would be 1/2 the original purchase price plus 1/2 the cost of any improvements done over time.
If your mother added you to the deed at some time after purchase, then your share was a gift and 1/2 your cost would be based on her original purchase price plus improvements
