Mệnh đề nào sau đây sai?\(\left| {f(x)} \right| = g(x) \Leftrightarrow \left[ \begin{array}{l} f(x) = g(x)\\ f(x) = - g(x) \end{array} \right.\)

A. \(\left| {f(x)} \right| = \left| {g(x)} \right| \Leftrightarrow {f^2}(x) = {g^2}(x)\)

B. \(\left| {f(x)} \right| = \left| {g(x)} \right| \Leftrightarrow \left[ \begin{array}{l}
f(x) = g(x)\\
f(x) =  - g(x)
\end{array} \right.\)

C. \(\left| {f(x)} \right| = g(x) \Leftrightarrow \left\{ \begin{array}{l}
g(x) \ge 0\\
\left[ \begin{array}{l}
f(x) = g(x)\\
f(x) =  - g(x)
\end{array} \right.
\end{array} \right.\)

D. \(\left| {f(x)} \right| = g(x) \Leftrightarrow \left[ \begin{array}{l}
f(x) = g(x)\\
f(x) =  - g(x)
\end{array} \right.\)