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If f: R^+vecR ,f(x)+3xf(1/x)=2(x+1),t h ...

If `f: R^+vecR ,f(x)+3xf(1/x)=2(x+1),t h e nfin df(x)dot`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=(x+1)//2`
`f(x)+3x f((1)/(x))=2(x+1) " (1)" `
Replacing `x` by `(1)/(x),` we get
`f((1)/(x))+3(1)/(x)f(x)=2((1)/(x)+1)`
or ` x f((1)/(x))+3f(x)=2(x+1) " (2)" `
From (1) and (2), we have `f(x)=(x+1)/(2).`
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