JEE Main 2022 (Online) 26th June Morning ShiftQuestion 1
Let $f(x)=\frac{x-1}{x+1}$, $x\in\mathbf{R}-\{0,-1,1\}$. If $f^{n+1}(x)=f(f^{n}(x))$ for all $n\in\mathbf{N}$, then $f^{6}(6)+f^{7}(7)$ is equal to :
Functions
Solution
$f^2(x)=-\frac1x$, $f^3(x)=\frac{1+x}{1-x}$, $f^4(x)=x$, period $4$. $f^6(6)=f^2(6)=-\frac16$, $f^7(7)=f^3(7)=\frac{8}{-6}=-\frac43$. Sum $=-\frac32$.