Finding input resistance for this circuit
If \$(1+RG) \neq 0\$, then the current is zero and so the input impedance in infinite. Otherwise the circuit doesn't have a unique solution.

To see this, note that \$i = -GV_x\$, where \$i\$ is the current entering the device. Since \$V_x = R i \$, this gives \$i = -GRi\$ or \$(1+RG) i = 0\$.