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Question

If a real value of function fof a real variable xis such that 1(1+x)(1+x2)=A(1+x)+f(x)(1+x2)then f(x)=


A

(1-x)2

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B

(x2+1)2

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C

1-x

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D

None of these

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Solution

The correct option is C

1-x


Explanation for the correct options:

Find the function f(x):

Given that a real value of function fof a real variable xis such that 1(1+x)(1+x2)=A(1+x)+f(x)(1+x2)

1=(1+x2)A+f(x)(1+x)

Put x=-1.we get

1=2AA=12

Now, 1(1+x)(1+x2)-12(1+x)=f(x)(1+x2)

1(1+x)2-1-x2(1+x2)=f(x)(1+x2)1-x2(1+x)=f(x)f(x)=(1-x)(1+x)(1+x)f(x)=(1-x)

Hence, the correct option is (C).


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