Let `f` be a real-valued function defined on the inverval `(-1,1)` such that `e^(-x)f(x)=2+int_0^xsqrt(t^4+1)dt ,` for all, `x in (-1,1)a n dl e tf^(-1)` be the inverse function of `fdot` Then `(f^(-1))^'(2)` is equal to 1 (b) `1/3` (c) `1/2` (d) `1/e`

Let f be a real-valued function on the interval (-1,1) such that e^(-x) f(x)=2+underset(0)overset(x)int sqrt(t^(4)+1), dt, AA x in (-1,1) and let f^(-1) be the inverse function of f. Then [f^(-1) (2)] is a equal to:

If the function f(x)=2-e^(-x) and g(x)=f^(-1)(x) , then the value of g"(1) is equal to -1 (b) 0 (c) 1 (d) 1/2

Let f(x) be a real valued function defined for all xge1 , satistying f(1)=1 and f'(x)=1/(x^(2)+(f(x))) , then lim_(xtooo)f(x)

If x!=1\ a n d\ f(x)=(x+1)/(x-1) is a real function, then f(f(f(2))) is (a) 1 (b) 2 (c) 3 (d) 4

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f\'(t))^2)dt=int_0^xf(t)dt, 0lexle1 and f(0)=0 , then (A) f(1/2)lt1/2 and f(1/3)gt1/3 (B) f(1/2)gt1/2 and f(1/3)gt1/3 (C) f(1/2)lt1/2 and f(1/3)lt1/3 (D) f(1/2)gt1/2 and f(1/3)lt1/3

f(x)=int_1^x lnt/(1+t) dt , f(e)+f(1/e)=