functions

**Punch** · April 10th 2011, 02:54 AM

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

**Prove It** · April 10th 2011, 03:15 AM

Are you allowed to use calculus?

**veileen** · April 10th 2011, 03:41 AM

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

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

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