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Math Help - Continuity Question

  1. #1
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    Continuity Question

    Let F(X) =

    5x-4, if x is less than or equal to 2

    -4x+b, if x is greater than 2

    If is a function which is continuous everywhere, then we must have b=_______?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by redraider717 View Post
    Let F(X) =

    5x-4, if x is less than or equal to 2

    -4x+b, if x is greater than 2

    If is a function which is continuous everywhere, then we must have b=_______?
    intuitively, what does continuous mean? it means there are no gaps, which means, we want -4x + b to pick up exactly where 5x - 4 left off.

    let f_1(x) = 5x - 4 and f_2(x) = -4x + b

    we want, f_1(2) = f_2(2)

    (yes, technically, x = 2 is not in the domain of f_2(x), but we do this because we want to get arbitrary close to x = 2)
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  3. #3
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    Given F(x) = \left\{ {\begin{array}{c}<br />
   {5x - 4,\;x \le 2}  \\<br />
   { - 4x + b,\;x > 2}  \\<br />
\end{array}} \right.

    You want: \lim _{x \to 2^ -  } F(x) = \lim _{x \to 2^ +  } F(x)
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