For x is greater than 3 , values of the function f of x is equal to negative open paren x minus 3 close paren squared times open paren x plus 2 close paren are negative. On this same interval, which statement correctly describes the values of the additive and multiplicative inverses?

For x > 3, (x − 3)² is positive and (x + 2) is positive, so f(x) = −(x − 3)²(x + 2) is negative. The additive inverse, −f(x), is therefore positive, while the multiplicative inverse, 1/f(x), is negative. This matches choice D: the additive inverse is positive, while the multiplicative inverse is negative.

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