`f(x)`is defined for `xge0` & has a continuous derivative. It satisfies `f(0)=1, f^(')(0)=0` & `(1+f(x))f^('')(x)=1+x`. The values `f(1)` can't take is/are

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

Explain whether f(x) is continuous and has a derivative at the point x=1 were f(x)=x for 0 1

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

Let f be a continuous function satisfying f'(In x)=[1 for 0 1 and f(0)=0 then f(x) can be defined as

If f(x) is a continuous function satisfying f(x)f(1/x) =f(x)+f(1/x) and f(1) gt 0 then lim_(x to 1) f(x) is equal to

Let f(x) be defined for all x>0 and be continuous.Let f(x) satisfy f((4x)/(y))=f(x)-f(y) for all x,y and f(4e)=1, then (a) f(x)=ln4x( b) f(x) is bounded (c) lim_(x rarr0)f((1)/(x))=0 (d) lim_(x rarr0)xf(x)=0

If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0 , then find the value of int_(0)^(a)(dx)/(1+f(x)) .

Suppose a continuous function f:[0,infty)rarrR satisfies f(x)=2int_0^xtf(t)dt+1 for all xge0 Then f(1) equals