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Question

# If 3f(x)+5f(1x)=1x−3, ∀x≠0 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+5x−6)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)=1x−3, 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)=1x−3,∀ x (≠0) ϵR ....(1) [Replacing x by 1x] ⇒3f(1x)+5f(x)=x−3 ...(2) Multiplying (1) by 3 and (2) by 5 subtracting, we get ⇒f(x)=116(−3x+5x−6),∀x(≠0ϵR.)

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