If `f(x)=(x-1)/(x+1),x!=-1,`. then show that `f(f(x))=-1/x`, prove tha – InterviewSolution

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1.	If `f(x)=(x-1)/(x+1),x!=-1,`. then show that `f(f(x))=-1/x`, prove that `x!=0`.
Answer» We have, `f(x)=(x-1)/(x+1)`, where `xne-1`. `:.f{f(x)}=f((x-1)/(x+1))={{(x-1)/(x+1)-1}/{(x-1)/(x+1)+1)}` `={{(x-1)-(x+1)}}/((x+1))xx(x+1)/{{(x-1)+(x+1)}}=(-2)/(2x)=(-1)/(x)`. Hence, `f{f(x)}=(-1)/(x)` where `xne0`.

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