Let `f:R-{0,1}rarr R` be a function satisfying the relation `f(x)+f((x-1)/(x))=x` for all `x in R-{0,1}` . Based on this answer the following questions. f(-1) is equal to

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

Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x))=1 for all x in[0,1] then:

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

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

Let f:[0,1] rarr R be a function.such that f(0)=f(1)=0 and f''(x)+f(x) ge e^x for all x in [0,1] .If the fucntion f(x)e^(-x) assumes its minimum in the interval [0,1] at x=1/4 which of the following is true ?

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) .

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =