InterviewSolution
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InterviewSolution
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If f' ((x)/(y)), f(x)/(y))=(x^(2)+y^(2))/(xy) AA x,y in R^(+) and f(1)=1, then f^(2) (x)is |
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Answer» `X+In x` Interchanging x,y we GET `f'((x)/(y)),f((y)/(x))=f'((y)/(x))f((x)/y)` `impliesInf((x)/(y))=INF((y)/(x))+C` Putting x=y,` we get `f'((x)/(y)).f((y)/(x))=f'((y)/(x))f((x)/(y))` `implies In f((x)/(y)) = In f((y)/(x))+C` Putting x=y, we get C=0 `impliesf((x)/(y))=f((y)/(x))...(ii)` Putting y=1, in equation (i) and (ii), we get `impliesf'(x)f((1)/(x)) =(x^(2)+1)/(x)` and `f(x)=f((1)/(x))` `impliesf'(x)f(x)=x+(1)/(x)` `implies (f(x))^(2)=x^(2)+2ln x` |
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