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Absolute value function

paulmdrdo

Active member
May 13, 2013
386
Define f(x)= |x+3|-|x-3| without absolute value bars piecewise in the following intervals (-∞,-3);[-3,3);[3,+∞).

this is how i do the problem,

I removed the absolute value bars first

f(x)= x+3-x+3 = 6

now i don't know how to define it piecewise. can you show me how define it correctly. thanks!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: absolute value function.

On the interval:

i) \(\displaystyle (-\infty,-3)\)

we have:

\(\displaystyle x+3<0\,\therefore\,|x+3|=-(x+3)\)

\(\displaystyle x-3<0\,\therefore\,|x-3|=-(x-3)\)

and so \(\displaystyle f(x)=(-(x+3))-(-(x-3))=-6\)

Can you try the other two intervals?