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

Let f(x)=|x-1|dot 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(w h e r ea >2)dotT h e nf(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+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

Which of the following functions have the graph symmetrical about the origin? (a) f(x) given by f(x)+f(y)=f((x+y)/(1-x y)) (b) f(x) given by f(x)+f(y)=f(xsqrt(1-y^2)+ysqrt(1-x^2)) (c) f(x) given by f(x+y)=f(x)+f(y)AAx , y in R (d) none of these

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

If f (x,y) =e ^(2x+3y) find 3f_(x) (0,0) - 2f_(y) (0,0):

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f''(x)=f(x)=0 (b) 4f''(x)+f(x)=0 (c) f''(x)+f(x)=0 (d) 4f''(x)-f(x)=0