If \( y=g(x) \) is the inverse of a bijective mapping \( f: R \rightarrow R \), \( f(x)=6 x^{5}+...

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If \( y=g(x) \) is the inverse of a bijective mapping \( f: R \rightarrow R \), \( f(x)=6 x^{5}+4 x^{3}+2 x \), find the area bounded by \( g(x) \), the \( x \)-axis and the ordinate at \( x=12 \).
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