Let $f:R\to R$ be a function such that $f\left(x\right)=\frac{x^2+2x+1}{x^2+1}$. Then

Let $f$ and $g$ be twice differentiable functions on $R$ such that

$f^{"}\left(x\right)=g^{"}\left(x\right)+6x$

$f^{\text{'}}\left(1\right)=4g^{\text{'}}\left(1\right)-3=9$

$f\left(2\right)=3 g\left(2\right)=12$

Then which of the following is NOT true ?

Consider a function $\mathrm{f}:\mathrm{\mathbb{N}}\to \mathrm{ℝ}$, satisfying $f\left(1\right)+2f\left(2\right)+3f\left(3\right)+\dots +xf\left(x\right)=x\left(x+1\right)f\left(x\right) ;x\ge 2$ with $f\left(1\right)=1$. Then $\frac{1}{f\left(2022\right)}+\frac{{\displaystyle 1}}{{\displaystyle f\left(2028\right)}}$ is equal to

Let $f^1\left(x\right)=\frac{3x+2}{2x+3},x\in R-\left\{-\frac{3}{2}\right\}$. For $n\ge 2$, define $f^n\left(x\right)=f^{1}o{f}^{n-1}\left(x\right)$. If $f^5\left(x\right)=\frac{ax+b}{bx+a}, \gcd \left(a,b\right)=1$, then $a+b$ is equal to ________