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Question

If f(x)=x1x+1, x1 then show that f(f(x))=1x, where x0).


Solution

We have, f(x)=x1x+1, where x1.

f{f(x)}=f(x1x+1)={x1x+11}{x1x+1+1}

={(x1)(x+1)}(x+1)×(x+1){(x1)+(x+1)}=22x=1x.

Hence, f{f(x)}=1x, where x0.

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