Hi all, If and are 3 continous functions on a set A, that verify: (beware the and not ) can I say that there exists such that: thank you Deubelte
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Let now define . Is that statement still true. You must have left something out of the statement of the question.
Originally Posted by deubelte If and are 3 continuous functions on a set A, that verify: (beware the and not ) can I say that there exists such that: No. Take and define , and (constant). Then (attained when x=10) and (attained when x=–10), so . But , and . So is always less than 1.01, which is less than .
I have an other question. supposing we have two continuous functions and such that: can I say that: there exists x in A such that: 1) 2) there exists x such that: thx
Originally Posted by deubelte I have an other question. supposing we have two continuous functions and such that: can I say that: there exists x in A such that: 1) 2) there exists x such that: Choose k with . Then there exists x in A such that . But , and therefore .
Ok, so I guess that my second statement is also true ?? Merci l'Anglais.
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