If k is given a real constant `f(x)` is a real quadratic in `x` such that `f(x+k)=f(-x)`. The coefficient of `x^(2)` is `1`, then find `f(x)`.

if f(x) be a quadratic polynomial such that f(2)=-3 and f(-2)=21 find the coefficient of x in f(x) .

Let f be a real-valued function such that f(x)+2f((2002)/(x))=3x. Then find f(x)

If f(x)=x^(2) is a real function, find the value of f(1).

If f(x) is real valued function such that (f(x-1)+f(x+1))/(2f(x))=sin60^(@),AA x in R then find the value of f(x-1)+f(x+5)

Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=sqrt(2)f(x) for all x in R , then ,

Given that f is a real valued differentiable function such that f(x) f'(x) lt 0 for all real x, it follows that

If f(x) satisfies the relation 2f(x)+(1-x)=x^(2) for all real x, then find f(x) .

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary. For function f(x) and g(x) which of the following is true (A) f(x)g(x)gt0 for all real x (B) f(x)g(x)lt0 for all real x (C) f(x)g(x)=0 for some real x (D) f(x)g(x)=0 for all real x

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary.Which of the following holds true? (A) g(0)g(1)lt0 (B) g(0)g(-1)lt0 (C) g(0)f(1)f(2)gt0 (D) f(0)f(1)f(2)lt0

Let f(x) be periodic and k be a positive real number such that f(x+k)+f(x)=0 for all x in R. Then the period of f(x) is