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Thread: functions

  1. #1
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    functions

    The function $\displaystyle f$ is defined by $\displaystyle f(x)=ln[(x-1)^2-k]$, where $\displaystyle x<-2$ and $\displaystyle k$ is a constant. Find the maximum value of $\displaystyle k$.

    what i did was:

    $\displaystyle [(x-1)^2-k]>0$ but since there're two unknowns, i couldn't solve it
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  2. #2
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    Are you allowed to use calculus?
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  3. #3
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    $\displaystyle x<-2\Rightarrow x-1<-3\Rightarrow (x-1)^2>9$
    $\displaystyle (x-1)^2-k>0\Rightarrow (x-1)^2>k$

    k has the maximum value $\displaystyle \Rightarrow k=9$
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