KVPY SX SB Exam 2012 Question Paper

Question : 90 of 120

Marks: +1, -0

Let

f(x)={x+1}/{x-1}

for all x ≠ 1. Let

f^1(x)=f(x),f^2(x)=f(f(x))

and generally

f^n(x)=f(f^{n-1}(x))

for n > 1
Let

P=f^1(2)f^2(3)f^3(4)f^4(5)

Which of the following is a multiple of P

Solution:

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=3×3×5/3×5=75

Multiple of P is 375

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