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

Let f be real-valued function such that f(2)=2 and f'(2)=1 then lim_(x rarr2)int_(2)^(f(x))(4t^(3))/(x-2)backslash dt is equal to :

Let f be a real valued function satisfying f(x)+f(x+6)=f(x+3)+f(x+9).Then int_x^(x+12)f(t)dt is

Let f(x) be a real valued function such that f(a)=0. If g(x)=(x-a)f(x) is continuous but notdifferentiable at x=a and h(x)=(x-a)^(2)f(x) is continuous and differentiable at x=a .Then f(x)

Let f be a real valued function such that for any real x f(15+x)=f(15-x)and f(30+x)=-f(30-x) Then which of the following statements is true ?

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

Let f be a real-valued invertible function such that f((2x-3)/(x-2))=5x-2,x!=2. Then value of f^(-1)(13) is

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

Let f be a real-valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) Prove that int_(x)^(x+8)f(t)dt is constant function.

Let f be a real valued function such that for any real x, f(lambda+x)=f(lambda-x) and f(2lambda+x)=f(2lambda-x) for some lambda>0 . Then

Let F be a real valued invertible function such that f((3x-5)/(x+2))=100x+13, x!=2 .Then find the value of f^(-1)(2013)