If `f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y)` is equal to : `f(x)f(y)` (b) `f(x)+f(y)` `f(x)-f(y)` (d) none of these

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1) then for x>0,y>0,f(xy) is equal to

Let f(x)=|x-1|* Then (a) f(x^(2))=(f(x))^(2) (b) f(x+y)=f(x)+f(y)(c)f(|x|)-|f(x)| (d) none of these

Given the function f(x)=(a^(x)+a^(-x))/(2)(wherea>2)dot Then f(x+y)+f(x-y)= (A) 2f(x).f(y) (B) f(x).f(y) (C) (f(x))/(f(y)) (D) none of these

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 (x+ y) = f(x) , f(y) , f(3) = 3 , f'(0) = 11 . Then f'(3) is equal to

Let f(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)], then (A) (f(x))^2=-I (B) f(x+y)=f(x),f(y) (C) f(x)^-1=f(-x) (D) f(x)^-1=f(x)

If f(x) is differentiable, then the solution of dy+f\'(x)(y-f(x))dx=0 is (A) yf(x)=Ce^(-f(f(x))^2) (B) y+1=f(x)+Ce^(-f(x)) (C) f(x)=Cye^(-y^2/2) (D) none of these