If non-zero real numbers $b$ and $c$ are such that $\min f ( x ) > \max g ( x )$, where $f ( x ) = x ^ { 2 } + 2 b x + 2 c ^ { 2 }$ and $g ( x ) = - x ^ { 2 } - 2 c x + b ^ { 2 } , ( x \in R )$; then $\left| \frac { c } { b } \right|$ lies in the interval\\
(1) $( \sqrt { 2 } , \infty )$\\
(2) $\left[ \frac { 1 } { 2 } , \frac { 1 } { \sqrt { 2 } } \right)$\\
(3) $\left( 0 , \frac { 1 } { 2 } \right)$\\
(4) $\left[ \frac { 1 } { \sqrt { 2 } } , \sqrt { 2 } \right]$