Let f ( x )=3+2 x and gn ( x )=( fo fo fo..... n times )( x ) . n ~N if all the lines y=g_ n (x) pass through a fixed point ( , ) , then + =

Step-by-step solution

f(x)=3+2 x g₁(x)=3+2 xg₂(x)=f f(x)=9+4 x g ₃(x)=f f f(x)=21+8 xg_n(x)=( fofof . . n times )(x)=3 (2^n-1 )+2^n x For fixed point x=y x=3 (2^ n -1 )+2^ n x x=-3 and y=3 (2^ n -1 )+2^ n x y=-3 So, (-3,-3) is a fixed point n N + =-3-3=-6