Let f, g and h be the real valued functions defined on R as f(x)={ x/(|x|), x ≠ 0; 1, x=0, g(x)= {(sin (x+1))/((x+1)), x ≠-1; 1, x=-1}. and…

Let $\displaystyle f, g$ and $\displaystyle h$ be the real valued functions defined on $\displaystyle \mathbb{R}$ as $$f(x)=\left\{\begin{array}{cc} \frac{x}{|x|}, & x \neq 0 \\ 1, & x=0 \end{array}, g(x)=\left\{\begin{array}{cc} \frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-1 \end{array}\right.\right. $$ and $\displaystyle h(x)=2[x]-f(x)$, where $\displaystyle [x]$ is the greatest integer $\displaystyle \leq x$.Then the value of $\displaystyle \lim _{x \rightarrow 1} g(h(x-1))$ is