If f(x) = `x / ( x - 1 ) = 1/y` , then f(y) is equal to

If f(x)=(x+2)/(x-1) then f(y) is equal to

If f(x) = (( x + 1))/( ( x - 1)) , then the ratio of x to f(y) where y = f(x) is

The solution of the differential equation ydx-(x+2y^(2))dy=0 is x=f(y). If f(-1)=1, then f(1) is equal to

If y=f(x) satisfies the differential equation (dy)/(dx)+(2x)/(1+x^(2))y=(3x^(2))/(1+x^(2)) where f(1)=1 , then f(2) is equal to

If f(x) be a differentiable function such that f(x+y)=f(x)+f(y) and f(1)=2 then f'(2) is equal to

If f(x)=(2^(x)+2^(-x))/(2), then f(x+y)f(x-y) is equals to (1)/(2){f(2x)+f(2y)}(b)(1)/(2){f(2x)-f(2y)}(c)(1)/(4){f(2x)+f(2y)}(1)/(4){f(2x)-f(2y)}

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and f(x)=1+xg(x) where lim_(x to 0) g(x)=1 . Then f'(x) is equal to