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Math Help - Continuous Function

  1. #1
    Junior Member
    Joined
    Nov 2008
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    37

    Continuous Function

    How to determine a and b so that function:

    <br />
 f(x) = <br />
\begin{cases}<br />
ax+b,  &  x\le -1,  \\<br />
4^x,  &  -1< x< 1, \\<br />
ax+b, & 1\le x <br />
\end{cases}<br />

    is continuous in all it's definition area?
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  2. #2
    Senior Member Twig's Avatar
    Joined
    Mar 2008
    From
    Gothenburg
    Posts
    396

    hi

    hi

    <br />
f(x) = <br />
\begin{cases}<br />
ax+b, & x\le -1, \\<br />
4^x, & -1< x< 1, \\<br />
ax+b, & 1\le x <br />
\end{cases}<br />

    Must have that  f(-1) = \frac{1}{4} , because
     4^{-1} = \frac{1}{4} .

    And  f(1) = 4

    This gives  \begin{cases} -a +b = \frac{1}{4} \\ a + b = 4 \end{cases}

     \Rightarrow \, a = \frac{15}{8} \mbox{ and } b = \frac{17}{8}
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  3. #3
    Junior Member
    Joined
    Nov 2008
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    Thank you for explanation.
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