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An expression is well-defined if you can compute its value without any illegal operations. Examples of expressions that are not well-defined include \(\frac{1}{0}\) and \(\sqrt{-10}\). For what values of \(\frac{\sqrt{4x + 1} - \sqrt{8 - 3x}}{\sqrt{2x - 5}}\) is the expression
well-defined?

Express your answer in interval notation.

 Apr 2, 2024
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sqrt [ 4x + 1]   not well defined whenever  x < -1/4           x ≥   -1/4

 

sqrt [ 8 -3x ]   not well defined when x > 8/3                     x ≤  8/3

 

sqrt [ 2x - 5 ]  in the  denominator  not well defined when x ≤  5/2              x > 5/2

 

The most restrictive interval is  (5/2 , 8/3 ]   { well-defined here }

 

 

cool cool cool

 Apr 2, 2024
edited by CPhill  Apr 2, 2024

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