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), a gt 2, then f (x+y) + f(x -y) =

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

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

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

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

Given the graph of y=f(x) . Draw the graphs of the followin. (a) y=f(1-x) (b) y=-2f(x) (c) y=f(2x) (d) y=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

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then