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

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

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`f(x)=(x-1)/(x+1)`
`implies" "f{f(x)}=(f(x)-1)/(f(x)+1)`
`=((x-1)/(x+1)-1)/((x-1)/(x+1)+1)=(x-1-x-1)/(x-1+x+1)`
`=(-2)/(2x)=01/x.`
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