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Question

Let f be a function satisfying 2f(x)3f(1x)=x2 for any x0, then the value of f(2) is

A
-2
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B
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C
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D
4
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Solution

The correct option is B
13(x2+4x3)2f(x)3f(1x)=x2(i)Replacing x by 1x2f(1x)3f(x)=1x2(ii)
Solving (i) and (ii) we get
5f(x)=2x2+3x2f(x)=15(2x2+3x2)f(2)=15(8+34)=74

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