If `f(x) =||x|-2|-2` for `x in [-4,4]` then the number of real solutions of `f(f(x))=-1` is

If f(x)=ln x then number of solutions of |f(|x|)|=4-x^(2) is

If f(x)={0,x<1 and 2x-2,x<=1 then the number of solutions of the equation f(f(f(x)))=x is

(a) If f(x)=-x|x| , then find f^(-1)(x) and hence find the number of solution of f(x)=f^(-1)(x) (b) Solve 2x^(2)-5x+2=(5-sqrt(9+8x))/4 , where xlt5/4

Let f(x) =ax^2+bx+c where a,b,c are real numbers. Suppose f(x)!=x for any real number x. Then the number of solutions for f(f(x))=x in real numbers x 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...... .

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...... .

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...... .

Let f (x) = x^(2)+10x+20. Find the number of real solution of the equation f (f (f (f(x))))=0

Let f (x) = x^(2)+10x+20. Find the number of real solution of the equation f (f (f (f(x))))=0