Particle in a potential well

A particle of mass m moves in the potential

V(x) = -g*delta(x)   x>-a
            infinity        x<-a


(delta (x) = dirac delta function)
a. Without worrying about continuity or boundary conditions, write down the general solution of the Schrodinger equation for a bound state (energy E<0) in regions( -a less than x less than 0) and x>0.

b. In terms of your solution in part (a), write down the boundary conditions at
x=-a and continuity conditions at x=0.

c. From the conditions in part (b), derive a transcendental  equation determining the bound state energy E. Solve the equation in the limit as a approaches infinity.