Function `f` satisfies the relation `f(x)+2f((1)/(1-x))=x AA x in R-{1,0}` then `f(2)` is equal to

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of lim_(x to -oo) f(x) is

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then Number of roots of the equation f(x)=e^(x) is

Consider the function f(x) satisfying the identity f(x) +f((x-1)/(x))=1+x AA x in R -{0,1}, and g(x)=2f(x)-x+1. The domain of y=sqrt(g(x)) is

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)) , AAx,y->R and f'(0)=0.Then f(6)is equal ______

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then