F

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...... .

If f(x)=a=b x+c x^2a n dalpha,beta,gamma are the roots of the equation x^3=1,t h e n|a b c b c a c a b| is equal to f(alpha)+f(beta)+f(gamma) f(alpha)f(beta)+f(beta)f(gamma)+f(gamma)f(alpha) f(alpha)f(beta)f(gamma) -f(alpha)f(beta)f(gamma)

If the function f: R-{(2005)/(153)}vecR-{(2005)/(153)} , defined by f(x)=(2005 x+153)/(153 x-2005) , then- (a) f^(-1)(x)=f(x) (b) f^(2014)(x)=x ,w h e r ef^n(x)=f(f(f(x)))n brackets (c)( f^(2013)(x)=x ,w h e r ef^n(x)=f(f(f(x)))n brackets (d) f^(-1)(x)=-f(x)