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Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f...

Let `f(x)=1/(1-x)` . Then, `{f\ o\ (f\ o\ f)}(x)=x` for all `x in R` (b) `x` for all `x in R-{1}` (c) `x` for all `x in R-{0,\ 1}` (d) none of these

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Verified by Experts

Given,
`f(x)=x/(1+x)​` and `g(x)=(rx)/(1−x)​`
`f(g(x))=f((rx)/(1−x)​​)=(rx)/(1−x+rx)`
​ And,
` g(f(x))=g(x/(1+x)​)=rx`
Now,
` f(g(x))=g(f(x))`
...
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