The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respectively, are:

In ion-exchange chromatography, a cation exchange resin must have acidic functional groups that can release $$\text{H}^+$$ ions and bind cations from the solution. The sulfonic acid group $$-\text{SO}_3\text{H}$$ is the standard functional group used in strongly acidic cation exchange resins.

An anion exchange resin must have basic functional groups that can release anions (such as $$\text{OH}^-$$) and bind anions from solution. The amino group $$-\text{NH}_2$$ (or quaternary ammonium groups) serves this purpose in anion exchange resins.

Therefore, the correct pair of functional groups responsible for the ion-exchange property of cation and anion exchange resins is $$-\text{SO}_3\text{H}$$ and $$-\text{NH}_2$$, respectively.