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

The number of solutions of log(2x)=2log(4x-15) is

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

Range of f(x)=ln(3x^(2)-4x+5) is

If f(x)=log_(x)(ln x) then f'(x) at x=e is

The number of solutions of the equation x^("log"sqrt(x)^(2x)) =4 is

f(x)=x(log x)^(2) then f is stationary at