Consider,`f(x) = tan^(-1)((sqrt(1+x^2)-1)/x) and g(x) = cosec^(-1) (sqrt(1+x^2)/x,x!=0` The number of solution of the equation `x^2=|f(x)-g(x)|`

Let f:R rarr R,f(x)=ln(x+sqrt(x^(2)+1)) and g:R rarr R,g(x)={x^((1)/(3)),x 1 then the number of real solutions of the equation,f^(-1)(x)=g(x) is

f(x)=1/abs(x), g(x)=sqrt(x^(-2))

f(x)=1/abs(x), g(x)=sqrt(x^(-2))

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...... .

f(x)=2x-tan^(-1)x-log(x+sqrt(1+x^(2)))(x>0) is increasing in

The number of real solutions of tan^(-1)sqrt(x^(2)+x)+ cosec^(-1)sqrt(1-x^(2)-x)=pi/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...... .

If f(x)=(x)/(sqrt(1-x^(2))), g(x)=(x)/(sqrt(1+x^(2))) then (fog)(x)=

If f(x)=(x)/(sqrt(1-x^(2))),g(x)=(x)/(sqrt(1-2x^(2))) then (gof) (x) is