Conformal map from a disk onto a disk with a slit

Question

Find a conformal mapping from D to $D\backslash [-1/2,1)$, where D is the unit disk. I think that maybe we can map $D\backslash [-1/2,1)$ to upper half plane first and the map upper half plane to $D$ and compute the inverses of the maps. Can we map $D\backslash [-1/2,1)$ to upper half plane? Thank you very much.