Question

If f(x)= x+1/x-1 show that x=f(y)

Answer 1

I am sure you meant:

f(x) = (x+1)/(x-1)
or
y = (x+1)/(x-1)

f(y) = ( (x+1)/(x-1) + 1) / ( (x+1)/(x-1) - 1)
multiply top and bottom by x-1
f(y) = ( x+1 + x-1) / ( x+1 - (x-1) )
= 2x/2
= x