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Question

Let R be the set of all real numbers and let f be a function R to R such that that f(x)+(x+12)f(1x)=1 for all x ϵ R.Then 2f(0)+3f(1)is equal to


A

2

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B

0

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C

-2

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D

-4

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Solution

The correct option is C

-2


Given f(x)+(x+12)f(1x)=1 ........(1)

But x=0

f(0)+12f(1)=1

2f(0)+f(1)=2 ............................... (2)

Put x=1 in (1)

f(1)+32f(0)=1

2f(1)+3f(0)=2 ............................. (3)

Solving (2) & (3) we have

f(0)=2 and f(1)=2

2f(0)+3f(1)=46=2


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