I'm just a bit confused as to how to solve this.

Interior point: There exists a z_0 E S if and only if there exists at least one neighbourhood of z_0 which is completely contained in S.

b) Let f: C - C be a continuous function, Z E C, and U S C. Prove that if f(z ) is an interior point of U then z is an interior point of the inverse image f-( U )