If `f(x)=(x-1)/(x+1),x!=-1,` then show that `f(f(x))=-1/x` provided that `x!=0,1.`

Explanation

`(f circ f) x=f(frac{x+1}{x-1})`
`=frac{frac{x+1}{x-1}+1}{frac{x+1}{x-1}-1} `
`
=frac{x+1+x-1}{x+1-x+1}`
`
=frac{2 x}{2}=x`


Now,
`

(f circ f circ f)(x)=f[f{f(x)}]=f(x)=frac{x+1}{x-1}`
`

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