$A=\left[\begin{array}{cc}1& \tan x\\ -\tan x& 1\end{array}\right]$ and $f\left(x\right)$ is defined as $f\left(x\right)=det.A^T{A}^{-1}$ then the value of $\frac{f\left(f\right(f......f\left(x\right)\left)\right))}{n\text{times}}(\text{for}n\ge 2)$ is

Q. $A=\left[\begin{array}{cc}1& \tan x\\ -\tan x& 1\end{array}\right]$ and $f\left(x\right)$ is defined as $f\left(x\right)=det.A^T{A}^{-1}$ then the value of $\frac{f\left(f\right(f......f\left(x\right)\left)\right))}{n\text{times}}(\text{for}n\ge 2)$ is

Q. $A=\left[\begin{array}{cc}1& \tan x\\ -\tan x& 1\end{array}\right]$ and $f\left(x\right)$ is defined as $f\left(x\right)=det.\left(A^T{A}^{-1}\right)$ then find the value of $\underset{\text{n times}}{\underset{}{f\left(f\right(f(f.......f(x\left)\right)\left)\right)}}$ is $(n\ge 2)$.

Q. Let the function $f\left(x\right)$ be defined as $f\left(x\right)=\{\begin{array}{c}{\tan }^{-1}\alpha -3x^2,0<x<1\\ -6x,x\ge 1\end{array}$

Q. If the function $f\left(x\right)$ is defined by $f\left(x\right)=a+bx$ and $f^r=fff....$ (repeated $r$ times), then $\frac{d}{dx}\left\{f^r\right(x\left)\right\}$ is equal to

Q. Consider the functions $f\left(x\right)$ and $g\left(x\right)$, both defined from $R\to R$ and are defined as $f\left(x\right)=2x-x^2$ and $g\left(x\right)=x^n$ where $n\in N$. If the area between $f\left(x\right)$ and $g\left(x\right)$ in first quadrant is $1/2$ then $n$ is not a divisor of :