Final answer:
To investigate when different cortical brain areas show value representation, one can use functional magnetic resonance imaging (fMRI) while performing a decision-making task related to value.
Step-by-step explanation:
To investigate when different cortical brain areas show value representation, one task and method that could be used is functional magnetic resonance imaging (fMRI) while performing a decision-making task related to value. For example, participants could be shown different options with varying values and asked to make choices. Brain activity can then be measured using fMRI to identify which areas of the cortex are active during value representation. This method allows researchers to understand how the brain processes and represents value.