Given the Polynomial Functions, Find the Product Function and the Specified

question 55

Multiple Choice

Given the polynomial functions, find the product function and the specified value.
-Let $f ( x ) = x + 3$ and $g ( x ) = x ^ { 2 } - 9 x - 7$ . Find $( f g ) ( x )$ and $( f g ) ( - 4 )$ .

• A) \(( f g ) ( x ) = 3 x ^ { 3 } + 27 x ^ { 2 } - 21 x ; ( f g ) ( - 4 ) = - 540\)
• B) \(( f g ) ( x ) = x ^ { 3 } + 12 x ^ { 2 } + 34 x + 21 ; ( f g ) ( - 4 ) = 285\)
• C) \(( f g ) ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 34 x - 21 ; ( f g ) ( - 4 ) = - 45\)
• D) \(( \mathrm { fg } ) ( \mathrm { x } ) = \mathrm { x } ^ { 3 } - 9 \mathrm { x } ^ { 2 } - 7 \mathrm { x } ; ( \mathrm { fg } ) ( - 4 ) = - 180\)

---

Definitions:

Archetypes

Universal, symbolic images or themes that recur across cultures and literature, representing fundamental human motifs or experiences.

Defence Mechanism

Psychological strategies used unconsciously by individuals to protect themselves from anxiety and to cope with reality or maintain self-image.

Identification

The process of associating oneself closely with other individuals or groups, often by adopting their characteristics or views.

Self-esteem

An individual's subjective evaluation of their own worth or value.