` f'(x^2) = 1/x` , `x>0 `, ` f(1) = 1` Find a function satisfying these conditions.

If f(x) is a polynomial function satisfying the condition f(x) .f((1)/(x)) = f(x) + f((1)/(x)) and f(2) = 9 then

If f(x) is a polynomial function satisfying the condition f(x) .f((1)/(x)) = f(x) + f((1)/(x)) and f(2) = 9 then

Let f(x) be a polynomial function of degree n satisfying the condition f(x)f((1)/(x))=f(x)+f((1)/(x)). Find f(x)

Does the function f(x) = {:{(x" if "x lt 1),(1//x " if "x ge1):} satisfy the conditions of the Lagrange theorem on the interval [0,2] ?

A function f satisfies the condition f(x) - f'(x) +f'(x) + f''(x) + ......, where f(x) is a differentiable function indefinitely and dash denotes the order of derivative . If f(0) =1 , then f(x) is

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^(2) .Prove that, int_(0)^(1)f(x)g(x)dx=(1)/(2)(2e-e^(2)-3)

If f(x) is an even function and satisfies the relation x^(2)f(x)-2f(1/x)=g(x),xne0 , where g(x) is an odd function, then find the value of f(2).

The function y=f(x) satisfying the condition f(x+1//x) =x^(3)+1//x^(3) is: