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: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

If f : R to R , f(x)=x^(2) and g(x)=2x+1 , then

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: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

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

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 :

(ii) Let g:R rarr R be defined as g(x)=(x^(3)+e^(2x)-1)/(2) . If g(f(x))=x while f((e^(4)+7)/(2))=alpha ,then find the number of solution(s) of the equation ||x-2|-3|-alpha=0

Let g:R rarr R be defined as g(x)=(x^(3)+e^(2x)-1)/(2). If g(f(x))=x while f((e^(4)+7)/(2))=alpha ,then find the number of solution(s) of the equation |x-2|-3|-alpha=0

Let f:R rarr R, f(x)=x+log_(e)(1+x^(2)) . Then