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The function f(x) < 0 when -2 < x < 1. Which of the following is true about the function |f(x) | ?

 

a) |f(x) | = - f(x) when -1 < x < 2

 

b) |f(x) | = f(x) when -1 < x < 2

 

c) |f(x) | = - f(x) when -2 < x < 1

 

d) |f(x) | = f(x) when -2 < x < 1

 Jan 24, 2022
 #1
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Options a and b are eliminated because we don't know anything about f(x) when x is in range -1 < x < 2.

 

Looking at c and d, we try to see which one makes sense. Because we know in this range of -2 < x < 1, f(x) will be negative, we can rewrite c and d.

c) = |f(x)| = f(x) because the -1 * -1 = 1

d) |f(x)| = -f(x) since f(x) in range -2 < x < 1 is negative.

 

Therefore the answer is c).

 Jan 24, 2022

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