Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be functions defined by $f(x)=\left\{\begin{array}{cl}x|x| \sin \left(\frac{1}{x}\right), & x \neq 0, \\ 0, & x=0,\end{array}\right.$ and $ g(x)=\left\{\begin{array}{cc} 1-2 x, & 0 \leq x \leq \frac{1}{2} \\ 0, & \text { otherwise } \end{array}\right. $ Let $a, b, c, d \in R$. Define the function $h: R \rightarrow R$ by $ h(x)=a f(x)+b\left(g(x)+g\left(\frac{1}{2}-x\right)\right)+c(x-g(x))+d g(x), x \in R $ Match each entry in List-I to the correct entry in List-II. The correct option is