How can I get symmetry equation of a function in proportion to an other one? for instance we know that: $y=\log_{10}{x}$ and $y=\log_{\frac{1}{10}}{x}$ are symmetric in proportion of $y=0$. now, I want a general solution for achieving this desired(in ex. $y=0$) for all function.
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1Can you give an example of a function $f$ that you don't know how to do this for? – Lopsy Feb 15 '15 at 16:11
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I want to do this for any function, I heard before about utility of Matrix in this matter, but I don't know how! – Alireza Ghaffari Feb 15 '15 at 16:13
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Assume you want to calculate the area under any function, if you want to do it by calculating manually it's miserable, but if you use integral operation,it'll so easy and general. – Alireza Ghaffari Feb 15 '15 at 16:15
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I wanted an example because I'm not sure what you mean. Probably English isn't your first language. Can you say what the answer for $y=\sin{x}$ is, or say what property it should satisfy? – Lopsy Feb 15 '15 at 16:18
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for example, &&y=\sin(x)&& and we have &y=x& then symmetry of &y=\sin(x)& will be &\asin(x)&. now think that we have &y=\sin(x)& and &\asin(x)&, I want to get &y=x& or even we have &y=\sin(x)& and &y=x& and I want to get &\asin(x)&. – Alireza Ghaffari Feb 15 '15 at 16:23