If `f: R^+vecR ,f(x)+3xf(1/x)=2(x+1),t h e nfin df(x)dot`

If f:R^(+)rarr R such that f(x)+4xf((1)/(x))=3((x+1)/(x)) then f(x)

If 5f(x)+3f((1)/(x))=x+2 and y=xf(x) then find (dy)/(dx) at x=1

f(x)+4xf((1)/(x))-3((x+1)/(x))

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

people living at Mars ,instead of the usual definition of derivative Df(x) define a new kind of derivative Df(x) by the formula Df(x)=lim_(h->0) (f^2(x+h)-f^2(x))/h where f^x means [f(x)]^2. If f(x)=xInx then Df(x)|_(x=e) has the value (a) e (b) 2e (c) 4e (d) non

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a)(f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c)f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

If f:R rarr R is a function such that f(x)=2^(x), find.(i) range of f( ii) (x:f(x)=1) (iii) f(x+y)=f(x)+f(y) is true or false.

f(x^(2)+x)+2f(x^(2)-3x+2)=9x^(2)-15x AA x in R find f(2016) Find f:R rarr R ,such that f(x)+xf(1-x)=1+x AA x in R