If `y=f(x)=(x+2)/(x-1) then prove that x=f(y)

If y=f(x)=(ax-b)/(bx-a) , the prove that : x=f(y)

If f(x) = y = (ax - b)/(cx - a) , then prove that f(y) = x.

If f(x)=log_(e)x, then prove that :f(xyz)=f(x)+f(y)+f(z)

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

If y = f(x) = (x+2)/(x-1) , x ne1 , then show that x = f(y) .

If f(x) = x/(x-1)=1/y then the value of f(y) is

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .

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)

Let f(x+y)=f(x)f(y) for all x,y in R and f(0)!=0 . Let phi(x)=f(x)/(1+f(x)^2) . Then prove that phi(x)-phi(-x)=0

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.