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

For each of the functions find the f _(x), f _(y), and show that f _(xy) = f _(yx). f (x,y) = cos (x ^(2) - 3xy )

In each of the following cases , determine whether the following function is homogeneous or not. If it is so , find the degree. (i) f(x,y)=x^2y+6x^3+7 (ii) h(x,y)=(6x^2y^3-piy^5+9x^4y)/(2020x^2+2019y^2) (iii) g(x,y,z)=(sqrt(3x^2+5y^2+z^2))/(4x+7y) (iv) U(x,y,z) =xy+sin((y^2-2z^2)/(xy))

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

For each of the functions find the f _(x), f _(y), and show that f _(xy) = f _(yx). f (x,y) = tan ^(-1)"" ((x)/(y))

A function f: RvecR satisfies the equation f(x)f(y)-f(x y)=x+yAAx ,y in Ra n df(1)>0 , then f(x)f^(-1)(x)=x^2-4 b. f(x)f^(-1)(x)=x^2-6 c. f(x)f^(-1)(x)=x^2-1 d. none of these

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

For each of the functions find the f _(x), f _(y), and show that f _(xy) = f _(yx). f (x,y) = (3x)/( y + sin x)

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2 , then