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Question

If af(x)+bf(1x)=x+5x;(ab) then f(x) equals.

A
1a2b2(x+1x)
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B
1a2b2[x(5ab)+1x(5ba)]
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C
1a2b2[x(a5b)+1x(5ab)]
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D
None of these
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Solution

The correct option is D 1a2b2[x(a5b)+1x(5ab)]
af(x)+bf(1x)=x+5x(i)
Put x=1x, we get
af(1x)+bf(x)=1x+5x(ii)
Multiplying (i) by a and (ii) by b and subtracting them, we get,
a2f(x)b2f(x)=ax+5axbx5bxf(x)=1a2b2[x(a5b)+1x(5ab)]

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