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Let f(x)=(x+1)/(x-1) for all xne1. Let ...

Let `f(x)=(x+1)/(x-1)` for all `xne1`. Let `f^(1)(x)=f(x),f^(2)(x)=f(f(x))` and generally `f^(n)(x)=f(f^(n-1)(x)) " for n"gt1` Let `P=f^(1)(2)f^(2)(3)f^(3)(4)f^(4)(5)` Which of the following is a multiple of P- (A) 125 (B) 375 (C) 250 (D) 147

A

125

B

375

C

250

D

147

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=(x+1)/(x-1)`
`f^(2)(x)=f(f(x))=f((x+1)/(x-1))=((x+1)/(x-1)+1)/((x+1)/(x-1)-1)=x`
`f^(3)(x)=f(x)=(x+1)/(x-1)`
`f^(4)(x)=x`
`P=f(2).f^(3)(3)f^(3)(4)f^(4)(5)`
`P=3xx3xx(5)/(3)xx5=75`
Multiple of P is 375
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