Problem Detail: For example if $$ f(x)= Theta (g(x)) $$ from the definition of the theta notation, there exist c1 and c2 constants such that $$c_1 g(x) le f(x) le c_2 g(x)$$ then if only we took the constants $1/c_1$ and $1/c_2$ we could say from the definition that $$ g(x)= Theta (f(x)) $$ Right?
Asked By : user65165
Answered By : David Richerby
Right, except that the constants are actually $1/c_2$ and $1/c_1$. That is, $$c_1 g(x) leq f(x) leq c_2g(x) Rightarrow frac{1}{c_2}f(x) leq g(x) leq frac{1}{c_1}f(x),.$$ Also, remember that the inequalities only apply for large enough $x$.
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Question Source : http://cs.stackexchange.com/questions/14339
