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

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

Which of the following functions have the graph symmetrical about the origin? f(x) given be f(x)+f(y)=f((x+y)/(1-xy))f(x) given by f(x)+f(y)=f(x sqrt(1-y^(2))+y sqrt(1-x^(2)))f(x) given by f(x+y)=f(x)+f(y)AA x,y in R none of these

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If f(x)=(a^(x)+a^(-x))/(2) and f(x+y)+f(x-y)=kf(x)f(y) then k=

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

Examples :- If x,y in {1;2;3;4} ;then which of the following are function in the given set ? (a) f_1={(x;y):y=(x+1)} (b) f_2={(x;y):x+y>4} (c) f_3={(x,y):y

If the function f:R rarr R defined by f(x)=(3^(x)+3^(-x)) , then show that f(x+y) = f(x-y) = 2f(x)f(y) .

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