If `f(x)f((1)/(x))=f(x)+f((1)/(x))AA x in R-[0},` where `f(x)` be a polynomial function and `f(5)=126,` then `f(3)=`

f(x+y)=f(x).f(y)AA x,y in R and f(x) is a differentiable function and f'(0)=1,f(x)!=0 for any x.Findf(x)

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

A polynomial function f(x) satisfies the condition f(x)f((1)/(x))=f(x)+f((1)/(x)) for all x in R,x!=0. If f(3)=-26, then f(4)=

If f (x) +2 f (1-x)( =x ^(2) +2AA x in R and f (x) is a differentiable function, then the vlaue of f'(8) is

f((x)/(y))=f(x)-f(y)AA x,y in R^(+) and f(1)=1, then show that f(x)=In x

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

let f(x) be a polynomial satisfying f(x) : f(1/x) = f(x) + f(1/x) for all XinR :- {O} and f(5) =126, then find f(3).

Let f(x)=x+f(x-1) for AA x in R.If f(0)=1, find f(100)

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