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

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 '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) .

The function f(x) satisfying the equation f^(2)(x)+4f'(x)f(x)+(f'(x))^(2)=0

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

If function f satisfies the relation f(x)*f'(-x)=f(-x)*f'(x) for all x and f(0)=3, and if f(3)=3, then the value of f(-3) is

If f satisfies the relation f(x+y)+f(x-y)=2f(x)f(y)AA x,y in K and f(0)!=0; then f(10)-f(-10)-

Let f be a differentiable function satisfying f '(x) =2 f(x) +10 AA x in R and f (0) =0, then the number of real roots of the equation f (x)+ 5 sec ^(2) x=0 ln (0, 2pi) is:

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 a function f(x) satisfies the relation 3f(x)-5f((2)/(x))=3-x+x^(2)AA x in R-{0} ,then the value of f(1) is equal to