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Question

If 3f(x)+5f(1x)=1x3 for all non-zero x, then f(x) =


  1. 114(3x+5x+6)

  2. 114(3x+5x6)

  3. 114(3x+5x6)

  4. None of these


Solution

The correct option is D

None of these


3f(x)+5f(1x)=1x3(1)
Multiplying (1) by 3:
15f(1x)+9f(x)=3x9(2)
Replacing x by 1x in (1):
3f(1x)+5f(x)=x3
Multiplying by 5:
15f(1x)+25f(x)=5x15(3)
Solving (2) and (3) :
16f(x)=3x5x+6f(x)=116(3x+5x6)  
(d) none of these

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