If the Function Is One-To-One, Find Its Inverse $$f ( x ) = 6 x ^ { 3 } + 4$$

question 114

Multiple Choice

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
- $$f ( x ) = 6 x ^ { 3 } + 4$$

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

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Definitions:

Density-Independent Factor

An environmental factor that affects the size of a population but is not influenced by changes in population density. Compare with density-dependent factor.

Killing Frost

A severe frost event causing significant damage or death to vegetation, effectively ending the growing season for many plants.

Density-Independent Factor

A factor that affects the size of populations regardless of their density, such as weather or natural disasters.

Predation

A biological interaction where a predator organism kills and consumes another organism known as the prey.