Printable View
hi!
this is the given function:
f(x) = |x+5|+ (|x^2+5x+6|/x)
i divided it up into sections:
f(x) = (x+5)+ (x^2+5x+6)/(x)) when -5<x<-3 x>-2
f(x)= -(x+5)+ (-(x^2+5x+6)/(x)) when x<-5 -3<x<-2
i was going to analyze these two functions but I'm confused.
could someone please help me?!?!?!
thanks!
Hello,Quote:
Originally Posted by Lilly100
use the definition of an absolute value:
$\displaystyle |x| = \left\{ \begin{array}{lcr}x&if&x\geq 0\\-x&if&x<0 \end{array}\right.$
With your problem you have the constraints:
$\displaystyle |x+5|= \left\{ \begin{array}{lcr}x+5&if&x\geq -5\\-(x+5)&if&x<-5 \end{array}\right.$.......... and
$\displaystyle |x^2+5x+6| = |(x+2)(x+3)|= \left\{ \begin{array}{rcl}x^2+5x+6x&if&x\leq -3~\vee~x\geq -2\\-(x^2+5x+6)&if&-3 < x -2 \end{array}\right.$
Additionally you have to observe that $\displaystyle x \neq 0$
Your function becomes:
$\displaystyle
f(x)=\left\{ \begin{array}{rcr}-(x+5)+\frac{x^2+5x+6}{x}&if&x <-5 \\ (x+5)+\frac{x^2+5x+6}{x}&if&-5 <x \leq -3 \\ (x+5)+\frac{-(x^2+5x+6)}{x}&if&-3 < x < -2 \\ (x+5)+\frac{x^2+5x+6}{x}&if& x\geq -2 \wedge x\neq 0 \end{array}\right.$
thanks for your reply!
Am I supposed to analyze the four different functions?
Hi,Quote:
Originally Posted by Lilly100
of course!
you can collect the summands but you have to observe the conditions quite carefully.
For instance:
$\displaystyle (x+5)+\frac{x^2+5x+6}{x}= \frac{x^2+5x+x^2+5x+6}{x}= \frac{2x^2+10x+6}{x}~,~x \geq-2 ~ \wedge ~ x\neq 0$
