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If f(x)=(1)/(1-x) then f[f{f(x)}]=...

If `f(x)=(1)/(1-x)` then f[f{f(x)}]=

A

6

B

-1

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`becauseg(x)=f{f(x)}=f((1)/(1-x))=(1)/(1-(1)/(1-x))=(x-1)/(x)`
and `h(x)=f[f{f(x)}]=f(g(x))`
`=(1)/(1-g(x))=(1)/(1-(x-1)/(x))=x`
`therefore f(x).g(x).h(x)=(1)/((1-x)).((x-1))/(x).x=-1`
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