Face verification involves identifying whether two faces belong to the same person or not. It relies heavily upon face perception, processing and the decision making of an individual. This research studies cross-domain face verification, where one face image belongs to a controlled, well-illuminated environment, while the other is of a varying representation having differences in image type or quality. Specifically, two cross-domain face verification tasks are analyzed: controlled-low resolution and controlled-sketch face verification. functional Magnetic Resonance Imaging (fMRI) data has been collected for 23 participants of two ethnic groups while performing face verification. Statistical comparisons were performed with same-domain controlled face verification for both the tasks. Our findings reveal regions of Right Frontal Gyrus, Bilateral Insula and Right Middle Cingulate Cortex demonstrating higher activation for controlled-sketch face verification, as compared to controlled face verification. Similar analysis were performed for controlled-low resolution face verification, where regions responsible for higher visual load and difficult tasks result in higher activation. Further, stimuli ethnicity differences influence activations for low-resolution face verification but do not affect sketch face verification. Regions of Right Middle Occipital Gyrus and Right Fusiform Gyrus present higher activity, suggesting increased face processing effort for within ethnicity low resolution face verification. We believe the findings of this research will help enable further development in the field of brain-inspired facial recognition algorithms.