Please help!

**rlarach** · January 2nd 2008, 10:07 AM

Consider the function f(x) = Log(1/2)(x^2 - 2x + 3) and determine :

( A ) Its domain.
( B ) The intervals where it is strictly increasing.
( C ) The intervals where it is strictly decreasing.

Thank you very much for your help!! I appreciate it!

**red_dog** · January 2nd 2008, 10:22 AM

$x^2-2x+3>0, \ \forall x\in\mathbf{R}$ .
So, the domain is $\mathbf{R}$ .

Let $g(x)=\log_{\frac{1}{2}}x$ and $h(x)=x^2-2x+3$ .
Then $f(x)=g(h(x))$
$g(x)$ is decreasing for all $x>0$ .
$h(x)$ is decreasing for all $x\leq 1$ and increasing for all $x\geq 1$ .
Then $f$ is increasing for all $x\leq 1$ and decreasing for all $x\geq 1$ .

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