SOLUTION: Determine the interval over which f(x)= the absolute value x-4 - the absolute value x+5 is a constant function.

Question 40809: Determine the interval over which f(x)= the absolute value x-4 - the absolute value x+5 is a constant function.
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
f(x) = |x-4| - |x+5|

When x<-5, |x-4| = -(x-4) = 4-x and |x+5| = -(x+5) = -x-5
So f(x) = |x-4| - |x+5| = 4-x+x+5 = 9

When -5 So f(x) = |x-4| - |x+5| = 4-x-x-5 = -2x-1

When 4 So f(x) = |x-4| - |x+5| = x-4-x-5 = -9

When x = -5, f(x) = |-5-4| = 9
When x = 4, f(x) = - |4+5| = -9

So f(x) = 9 when x <= -5
and f(x) = -9 when x >= 4

Thus the interval in which f(x) is constant is x <= -5 and x >= 4.
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