Find the Requested Composition of Functions $f ( x ) = x ^ { 2 } + 8$

question 59

Multiple Choice

Find the requested composition of functions.
-Given $f ( x ) = x ^ { 2 } + 8$ and $g ( x ) = x ^ { 2 } - 8$ , find $f g ( x )$ .

• A) \(x ^ { 4 } - 16 x ^ { 2 } + 72\)
• B) \(x ^ { 4 } + 16 x ^ { 2 } + 72\)
• C) \(x ^ { 4 } + 16 x ^ { 2 } + 56\)
• D) \(x ^ { 4 } - 16 x ^ { 2 } + 56\)

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Definitions:

Hindbrain

A region at the lower back part of the brain that controls basic life functions like breathing and heart rate, and includes structures like the cerebellum and medulla oblongata.

Midbrain

A key area located within the brainstem, crucial for coordinating motor movements, especially eye movements, and involved in processing sound and visual information.

Forebrain

The anterior part of the brain, including the cerebral hemispheres, thalamus, and hypothalamus, responsible for cognitive, sensory, and motor functions.

Cortex

The outermost layer of the brain, involved in complex functions such as perception, thought, and voluntary movement.