# Math Help - functions

1. ## 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

2. Are you allowed to use calculus?

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

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