Let `f: R->R ,f(x)=ln(x+sqrt(x^2+1)) and g: R->R ,g(x)={x^(1/3),xle=1 and 2e^(1-x),x >1,` then the number of real solutions of the equation, `f^-1(x)=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_(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 :R ->R , f(x)=x^3 +3 ,and g:R->R , g(x)=2x + 1 , then f^(-1)(g^(-1)(23)) equals

If f :R ->R , f(x)=x^3 +3 ,and g:R->R , g(x)=2x + 1 , then f^(-1)(g^(-1)(23)) equals

If f :R ->R , f(x)=x^3 +3 ,and g:R->R , g(x)=2x + 1 , then f^(-1)g^(-1)(23) equals

Let f:R -{3} to R{1} : f(x) = (x-2)/(x-3)and g:R to R , g(x)=2x-3 and f^-1(x)+g^-1(x)=13/2 then sum of all value of x is

Let f:R→R: f(x)=x+1 and g:R→R: g(x)=2x−3 . Find (f−g)(x) .

If f : R to R , f (x) =x ^(3) and g: R to R , g (x) = 2x ^(2) +1, and R is the set of real numbers then find fog(x) and gof (x).

Let f:R rarr R be defined by f(x)=In(x+sqrt(x^(2)+1)), then number of solutions of |f^(-1)(x)|=e^(-|x|) is :