Question 859694: Hi there again! Keeping with my schedule with pre-calculus learning, now i'm struggling with a problem on absolute value function. Said function is this one:
f(x) = ||3x + 2| - 3|
Its an absolute value inside another absolute value!!! I stopped when i got this absolut value of a piecewise function:
g(x) =
| 3x - 1 if x >= 1/3 |
| -3x + 5 if x < 1/3 |
So, any help or hint on how to work this out i would be glad!!
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! This is not a full solution, but it should at least help you to understand the given function better.
The function will be positive, regardless of the x value used.
Deep inside, 3x+2=0 when?
3x+2=0 at  , may be a critical point.
Out from that by one level, when does  ?
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If x<0 then -3x-2=3,
 , a critical point.
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If x>=0 then 3x+2=3,
 , a critical point.
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The three different critical points cut the x axis into four intervals, and you can find what the function definition would be in each interval, without expressing the function definition parts in absolute value.
Summary of the intervals based on these critical points:
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