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

If f: RvecR is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

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________

Statement 1: Let f: RvecR be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

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.

If f is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) is

Consider the real-valued function satisfying 2f(sinx)+f(cosx)=xdot then the (a)domain of f(x)i sR (b)domain of f(x)i s[-1,1] (c)range of f(x) is [-(2pi)/3,pi/3] (d)range of f(x)i sR

Let f(x) be a function such that f(x)=(log)_(1/2)[(log)_3(sinx+a]dot If f(x) is decreasing for all real values of x , then a in (1,4) (b) a in (4,oo) a in (2,3) (d) a in (2,oo)

Let f(x)=tanxa n dg(f(x))=f(x-pi/4), where f(x)a n dg(x) are real valued functions. Prove that f(g(x))="tan ((x+1)/(x+1))dot

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3),x in R . Then f(2) equals