Which one of the following function(s) is/are homogeneous? `(a) f(x,y)= (x-y)/(x^2 + y^2)` (b) `f(x,y)= x^(1/3)y^(-2/3)tan^-1(x/y)` (c) `f(x,y)=x(lnsqrt(x^2+y^2)-lny)+ye^(x/y)` (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

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

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

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)= 2f(x)dotf(y) (b) f(x)dotf(y) (f(x))/(f(y)) (d) none of these

If f(x+y,x -y)= xy then (f(x,y)+f(y,x))/(2)=

If f(x)=lim_(n->oo)n(x^(1/n)-1),then for x >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

Find f(x, y) if f(x + 2y, 2x + y) = 2xy.

Which one of the following is not a function? {(x , y): x , y in R , x^2=y} b. {(x , y): x , y in R , y^2=x} c. {(x , y): x , y in R , x=y^3} d. {(x , y): x , y in R , y=x^3}

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then