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 $f(x)$.
How to solve for $x$ when given function is $f(\ln(x))$
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algebra-precalculus
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0Using 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... – 2012-06-19
2 Answers
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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 $y^2-4$