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Question

If 3fx+5f1x=1x-3 for all non-zero x, then f(x) =

(a) 1143x+5x-6
(b) 114-3x+5x-6
(c) 114-3x+5x+6
(d) None of these

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Solution

(d) None of these

3fx+5f1x=1x-3 ...(1)

Multiplying (1) by 3:15 f1x +9 f(x) = 3x-9 .....(2)Replacing x by 1xin (1):3 f1x +5 f(x) = x-3 Multiplying by 5:15 f1x +25 f(x) = 5x-15 ....(3)Solving (2) and (3):-16 f(x) = 3x-5x+6f(x) = 116-3x+5x-6
Disclaimer: The question in the book has some error, so, none of the options are matching with the solution. The solution is created according to the question given in the book.

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