Let $f:\left(-\frac{\pi }{2},\frac{\pi }{2}\right)\to R$ be given by $f\left(x\right)={\left[\log \left(\sec x+\tan x\right)\right]}^3.$ Then,

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