Determine Whether the Given Function Is One-To-One $$f ( x ) = 6 x ^ { 3 } + 4$$

question 12

Multiple Choice

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
- $$f ( x ) = 6 x ^ { 3 } + 4$$

• A) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 4 } { 6 } }\)
• B) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 4 } { 6 } }\)
• C) Not a one-to-one function
• D) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 6 } } - 4\)

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Definitions:

White matter

Tissue in the brain and spinal cord made up primarily of nerve fibers and is responsible for communication between different brain regions and between the brain and the spinal cord.

Neurotransmitter

A chemical within the vesicles of the synaptic knob that is released into the postsynaptic structures when a nerve impulse reaches the synaptic knob.

Synaptic knob

The expanded region at the end of an axon terminal, where neurotransmitters are released to communicate with other neurons or muscle cells.

Interneuron

A type of neuron that communicates only with other neurons, typically found within the central nervous system and plays a role in reflexes and neuronal circuits.