Find all intervals on which f(x) = |x − 4| − |x + 4| is decreasing.

Find all intervals on which
f(x) = |x − 4| − |x + 4|
is decreasing.
1. no interval
2. (−4, 1)
3. (−1, −4)
4. (−1, −4) , (4, 1)
5. (−4, 4)
6. (4, 1)
7. (−1, 4)
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1 Answer

Answer 5.

When x≤-4 f(x)=8

When -4≤x≤4 f(x)=-2x (f(x)=-(x-4)-(x+4)=-x+4-x-4=-2x)

When x≥4 f(x)=-8

So f(x) decreases for -4≤x≤4.

by Top Rated User (1.2m points)

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