Let `f` be a one-one function satisfying `f'(x)=f(x)` then `(f^-1)''(x)` is equal to

If f is one-one and satisfies f'(x)=sqrt(1-(f(x))^(2)) then (f^(-1))'(x)

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2) . Then the value of the integral int_(0)^(1) f(x)g(x) dx is equal to -

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^(2) .Prove that, int_(0)^(1)f(x)g(x)dx=(1)/(2)(2e-e^(2)-3)

For x in RR - {0, 1}, let f_1(x) =1/x, f_2(x) = 1-x and f_3(x) = 1/(1-x) be three given functions. If a function, J(x) satisfies (f_2oJ_of_1)(x) = f_3(x) then J(x) is equal to :

For x in RR - {0, 1}, let f_1(x) =1/x, f_2(x) = 1-x and f_3(x) = 1/(1-x) be three given functions. If a function, J(x) satisfies (f_2oJ_of_1)(x) = f_3(x) then J(x) is equal to :

Let f be a continuous function satisfying f(x + y) = f (x) f( y) (x, y in R) with f(1) = e then the value of int(xf(x))/(sqrt(1+f(x)))dx is