Let $X$ be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $\alpha$ is the number of one-one functions from $X$ to $Y$ and $\beta$ is the number of onto function form $Y$ to $X,$ then the value of $\frac{1}{5!}\left(\beta -\alpha \right)$ is

Let $f$, be a function defined by $f\left(x\right)={\left(x-1\right)}^2+1, \left(x\ge 1\right)$

Statement -$1:$ The set $\left\{x: f\left(x\right)=f^{-1}\left(x\right)\right\}=\left\{1, 2\right\}$
Statement - $2: f$, is a bijection and $f^{-1}\left(x\right)=1+\sqrt{x-1}, x\ge 1$

For $x\in R, f\left(x\right)=\left|\log 2-\sin x\right|$ and $g\left(x\right)=f\left(f\left(x\right)\right),$ then

Let $f\left(x\right)=\left\{\begin{array}{ll}-1,& -2\le x<0\\ x^2-1,& 0\le x\le 2\end{array}\right.$ and $g\left(x\right)=\left|f\right(x\left)\right|+f\left(\right|x\left|\right).$ Then, in the interval $(-2, 2), g$ is