For x > 3, values of the function f(x) = –(x – 3)2(x + 2) are negative. On this same interval, which statement correctly describes the values of the additive and multiplicative inverses?
Answer
A
Both the additive inverse and the multiplicative inverse are positive.
B
Both the additive inverse and the multiplicative inverse are negative.
C
The additive inverse is positive, while the multiplicative inverse is negative.
D
The additive inverse is negative, while the multiplicative inverse is positive.
Explanation
For every x > 3, the question states that f(x) is negative. The additive inverse is −f(x), which is positive because it changes the sign. The multiplicative inverse is 1/f(x), which remains negative because the reciprocal of a negative number is negative. Therefore, the additive inverse is positive and the multiplicative inverse is negative (choice C).
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