Question

If f(x)=x+1/x-1,then prove that f{f(x)}=x

Answer 1

Here value of f(x) = x+1/x-1
similarily ,
f{f(x)} = (x+1/x-1) +1 / (x+1/x-1) -1
= (x+1+x-1)/( x-1) / (x+1-x+1) / (x-1)
= 2x/(x-1) /2/(x-1)
Now canceling x-1 from x-1
= 2x/2
= x
So, f{f(x)} = x
hence proved