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Question

If f(x)=x1x+1, then f(2x) is

A
f(x)+1f(x)+3
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B
3f(x)+1f(x)+3
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C
f(x)+3f(x)+1
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D
f(x)+33f(x)+1
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Solution

The correct option is B 3f(x)+1f(x)+3
We have f(x)=x1x+1...(i)
f(x)+1f(x)1=2x2
(applying componendo-dividendo)
x=f(x)+11f(x)....(ii)
Now, f(2x)=2x12x+1=2(f(x)+11f(x))12(f(x)+11f(x))+1=3f(x)+1f(x)+3

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