I need to answer this question, but I don't even clearly understand what is wanted: for approximation problem on $[a,b]$ show a linear map $x \rightarrow t$ that shows it is equivalent to same approximation problem on interval $[-1,1]$ or $[0,1]$ and show how both the function and norm change. Thanks.
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There is not enough information to understand what the problem is. – copper.hat Apr 10 '22 at 19:23
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@copper.hat Unfortunately, that's the entire text of the problem, and it is unclear to me what is expected. That's why I posted here, assuming there is some reading between the lines skill I don't have yet. – abenol Apr 10 '22 at 20:48
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Sorry, nothing rings a bell for me. – copper.hat Apr 10 '22 at 20:53