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Math Help - functions

  1. #1
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    functions

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

    what i did was:

    [(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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    x<-2\Rightarrow x-1<-3\Rightarrow (x-1)^2>9
    (x-1)^2-k>0\Rightarrow (x-1)^2>k

    k has the maximum value \Rightarrow k=9
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