This Paper presents an efficient approach for the fast computation of inverse continuous time variant functions with the proper use of Radial Basis Function Networks (RBFNs). The approach is based on implementing RBFNs for computing inverse continuous time variant functions via an overall damped least squares solution that includes a novel null space vector for singularities prevention. The singularities avoidance null space vector is derived from developing a sufficiency condition for singularities prevention that conduces to establish some characterizing matrices and an associated performance index.