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Q.

If f(x)2     f1-x1+x= x3 ,  x≠ -1 , 1 and f(x)≠0 , then {f(-2)} (the fractional part of  f(-2) is equal to

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a

2 /3

b

1/ 3

c

1/ 2

d

0

answer is A.

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Detailed Solution

Replacing x by 1-x1+x in the equation (f(x))2f1−x1+x=x3                   …(i)we have  f1−x1+x2f(x)=1−x1+x3       …(ii)solving (i) and (ii), we have x3(f(x))2  f(x) = 1-x1+x3⇒        (f(x))3x6=1-x1+x3⇒        f(x) = x21+x1-x             f(-2)=4-13=-43{f(-2)} = -43--43 =-43+2=23
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