Let f(x) be polynomial function of defree 2 such that `f(x)gt0` for all `x in R.` If `g(x)=f(x)+f'(x)+f''(x)` for all x, then

Let f(x) be a polynomial of degree two which is positive for all x in R. If g(x)=f(x)+f(x)+f'(x)+xf''(x)+x^(2)f^(iv)(x) then for any real x,prove that g(x)>0

Let f be a polynomial function such that f(3x)=f'(x);f''(x), for all x in R. Then : .Then :

Let f be a function from a set X to X, such that (f(f(x)) = x, for all x in X , then

Given that f(x) gt g(x) for all x in R and f(0) =g(0) then

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x^(2)+3x)g(x) for all x, where g(x) is continuous and g(0)=3 . Then find f'(x) .

Let f be a function such that f(x+y)=f(x)+f(y)" for all "x and y and f(x) =(2x^(2)+3x) g(x)" for all "x, " where "g(x) is continuous and g(0) = 3. Then find f'(x)

let f(x) be the polynomial function. It satisfies the equation 2 +f(x)* f(y) = f(x) + f(y) +f(xy) for all x and y. If f(2) =5 find f|f(2)| .

Let f be a differentiable function such that f(0)=e^(2) and f'(x)=2f(x) for all x in R If h(x)=f(f(x)) ,then h'(0) is equal to