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Question

If 3f(x)+5f(1x)=1x3,
x0 ϵR,then f(x)=

A
116(3x+5x6)
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B
116(3x+5x6)
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C
114(3x+5x6)
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D
None of these
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Solution

The correct option is B 116(3x+5x6)
Best way to solve this kind of problem is by checking options by putting different values of x.
For x = 1, given equation
3f(x)+5f(1x)=1x3, gives f(1)=14
Put x = 1 in different options and see which option gives f(1)=14
Option (b) is equal to 14 for x = 1, hence is the correct answer.

Conventional Approach:
We have, 3f(x)+5f(1x)=1x3, x (0) ϵR ....(1)
[Replacing x by 1x]
3f(1x)+5f(x)=x3 ...(2)
Multiplying (1) by 3 and (2) by 5 subtracting, we get
f(x)=116(3x+5x6),x(0ϵR.)

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