If `f(x) = (x-1)/(x+1)`, then show that `f(1/x) = -f(x) and f(-1/x) = -1/(f(x))`

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

If f(x) = x/(x-1) , then show that fof (x) = x.

If f(x) = (x-1)/(x+1) , x ne -1 then show that f(f(x)) =(-1)/x

If f(x) =x/(x-1) then show that (fof)(x) = x.

If f(x) = (1)/(1-x) , show that f(f(x)) = x

If ‘f’ is a real function defined by : f(x)= (x-1)/(x+1) , then prove that f (2x) = (3 f(x)+1)/(f(x)+3) .

if f(x) = (x-1)/(x+1), x ne -1 , then show that : f(f(x)) = -1/x, x ne 0 .

If f(x) = log ((1-x)/(1+x)) -1 lt x lt 1 then show that f(-x) = -f (x)

If f(x) = (x+2)/(3x-1) then f (f(x)) is