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`

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the function f(x)dot

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

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

Let f: R^+ ->R be a function which satisfies f(x)dotf(y)=f(x y)+2(1/x+1/y+1) for x , y > 0. Then find f(x)dot

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,t h e nfin df(6)dot

f(x) = x^(x)+ x^(1/x), find f'(x).