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Let f(x)=x/(1+x) " and " g(x)=(rx)/(1-x)...

Let `f(x)=x/(1+x) " and " g(x)=(rx)/(1-x).` Let S be the set of all real numbers r , such that f(g(x))=g(f(x)) for infinitely many real numbers x. The number of elements in set S is

A

1

B

2

C

3

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
`f(g(x))=(rx)/(1+(r-1)),g(f(x))=rx.`
`"If "f(g(x))=g(g(x))`
`rArr" "(rx)/(1+(r-1)x)=rx`
`rArr" "rx[1-(1)/(1+(r-1)x)]=0`
If this is to ture for infinitely many (all) x, then r = 0 or r-1 = 0
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