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Someone asked me this question and I need a solution. If $$f(\ln(x))=x^2$$ and $$f(x+1/x)=x-\frac{1}{x}$$ then find $f(x)$.

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Using more words in your questions would do well for the quality standard. Also, writing mathematical expressions in within \$\$s. Also, properly tagging them. It's not a diophantine equation... –  tomasz Jun 19 '12 at 22:16

2 Answers 2

Hints: for the first, let $y=\exp(x)$. For the second, let $y=x+\frac 1x$ (assuming that is the argument of the function, and not $\frac {x+1}x$. Please use parentheses when writing inline. Are these truly diophantine equations, in which case the variables must be integers? I suspect not.

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hint 1: set $y:=\ln x$ for the first and $y:=x+\frac 1x$ for the second.

hint 2: for the second consider $y^2-4$

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