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 f(x) = cos(log x) then f(x)f(y)-1/2[f(x/y)+f(xy)] has the value

If f(x)=cos((log)_e x),\ t h e n\ f(1/x)f(1/y)-1/2{f(x y)+f(x/y)} is equal to a. "cos"(x-y) b. log(cos(x-y)) c. 0 d. "cos"(x+y)

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

If f(x)=cos(logx) , then prove that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/(y))+f(xy)]=0

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

If f(x)=(log)_x(log x),t h e nf^(prime)(x) at x=e is equal to (a) 1/e (b) e (c) 1 (d) zero

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (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

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