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

If `f(x)=(x-1)/(x+1)` , then show that `f(1/x)=-f(x)` (ii) `f(-1/x)=1/(f(x))`

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We have `f(x)=(x-1)/(x+1)`
`f((1)/(x))=((1)/(x)-1)/((1)/(x)+1)=((1-x)//x)/((1+x)//x)=(1-x)/(1+x)=(-(x-1))/(x+1)=-f(x)`
(ii) `f((-1)/(x))=(-(1)/(x)-1)/(-(1)/(x)+1)=((-1-x)//x)/((-1+x)//x)rArrf(-(1)/(x))=(-(x+1))/(x-1)`
Now, `(-1)/(f(x))=(-1)/((x-1)/(x+1))=(-x(x+1))/(x-1)`
`:. f(-(1)/(x))=-(1)/(f(x))`
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