Let `f(x)=ax+b` with `a,b in R, ``f_(1)(x)=f(x)` and `f_(n+1)(x)=f(f_(n)(x)), If ``f_(7)(x)=128x+381` Then `a+b` is

Let f(x) = x - [x] , x in R then f(1/2) is

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

For x in R , x ne0, 1, let f_(0)(x)=(1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)),n=0,1,2….. Then the value of f_(100)(3)+f_(1)((2)/(3))+f_(2)((3)/(2)) is equal to

Let f(x)=(3)/(4)x+1,f^(n)(x) be defined as f^(2)(x)=f(f(x)), and for n ge 2, f^(n+1)(x)=f(f^(n)(x))." If " lambda =lim_(n to oo) f^(n)(x), then

Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

Let f(x)=(1)/(1+x) and let g(x,n)=f(f(f(….(x)))) , then lim_(nrarroo)g(x, n) at x = 1 is

Let f_(1) : R to R, f_(2) : [0, oo) to R, f_(3) : R to R be three function defined as f_(1)(x) = {(|x|, x < 0),(e^x , x ge 0):}, f_(2)(x)=x^2, f_(3)(x) = {(f_(2)(f_1(x)),x < 0),(f_(2)(f_1(x))-1, x ge 0):} then f_3(x) is:

If f_1(x)=(1)/(x), f_(2) (x)=1-x, f_(3) (x)=1/(1-x) then find J(x) such that f_(2) o J o f_(1) (x)=f_(3) (x) (a) f_(1) (x) (b) (1)/(x) f_(3) (x) (c) f_(3) (x) (d) f_(2) (x)

Let f :R -{(3)/(2)}to R, f (x) = (3x+5)/(2x-3).Let f _(1) (x)=f (x), f_(n) (x)=f (f _(n-1) (x))) for pige 2, n in N, then f _(2008) (x)+ f _(2009) (x)=