JEE 2023 — Mathematics PYQ

Let $f,g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as: $f(x)=\{\begin{array}{ll}\frac{x}{|x|},& amp;x\ne 0\\ 1,& amp;x=0\end{array},g(x)=\{\begin{array}{ll}\frac{\sin (x+1)}{(x+1)},& amp;x\ne -1\\ 1,& amp;x=-1\end{array}$ and $h(x)=2[x]-f(x)$, where $[x]$ is the greatest integer $\le x$. Then the value of ${\lim }_{x\to 1}g(h(x-1))$ is: