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) \(( \mathrm { fg } ) ( \mathrm { x } ) = \mathrm { x } ^ { 3 } - 9 \mathrm { x } ^ { 2 } - 7 \mathrm { x } ; ( \mathrm { fg } ) ( - 4 ) = - 180\)

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Definitions:

The Basal Ganglia

A group of structures in the brain involved in processing information related to movement, emotions, and learning.

Semipermeable

A type of membrane that allows certain substances to pass through it while blocking others, often used in biological and chemical contexts.

Cell Membranes

The semipermeable membranes that surround cells, controlling the movement of substances in and out of the cell.

Broca's

Refers to Broca's area, a region in the frontal lobe of the brain associated with language production and processing.