Let `f(x)=((2008)^x+(2008)^(-x))/2,g(x)=((2008)^x-(2008)^(-x))/2` then prove that `f(x+y)=f(x)f(y)+g(x)g(y)`

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If f(x) = 1/2 (3^x + 3^(-x)), g(x) = 1/2 (3^x - 3^(-x)) , then f(x) \ g(y)+f(y) \ g(x)=

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).

If f(x) = x^(2) and g(x) = (1)/(x^(3)) . Then the value of (f(x)+g(x))/(f(-x)-g(-x)) at x = 2 is

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

Let f and g be two differentiable functins such that: f (x)=g '(1) sin x+ (g'' (2) -1) x g (x) = x^(2) -f'((pi)/(2)) x+ f'(-(pi)/(2)) If phi (x) =f ^(-1) (x) then phi'((pi)/(2) +1) equals to :

Let f :R -{(3)/(2)}to R, f (x) = (3x+5)/(2x-3).Let f _(1) (x)=f (x), f_(n) (x)=f (f _(n-1) (x))) for pige 2, n in N, then f _(2008) (x)+ f _(2009) (x)=