The Function F Is One-To-One $$f ( x ) = \frac { 2 } { x - 4 }$$

question 370

Multiple Choice

The function f is one-to-one. Find its inverse.
- $$f ( x ) = \frac { 2 } { x - 4 }$$

• A) \(f ^ { - 1 } ( x ) = \frac { - 4 + 2 x ^ { 2 } } { x }\)
• B) \(f ^ { - 1 } ( x ) = \frac { - 4 + 2 x } { x }\)
• C) \(f ^ { - 1 } ( x ) = \frac { x } { - 4 + 2 x }\)
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 2 } { \mathrm { x } }\)

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Definitions:

Ampulla

An enlargement or dilatation in a canal or duct, commonly referring to the dilated end of ducts such as the bile duct.

Utricle

A part of the inner ear's vestibular system, responsible for detecting linear accelerations and head position changes.

Vestibule

An entryway or small room between the outer door and the interior of a building, or an anatomical space within the body, especially within the ear or nose.

Inner Ear

The innermost part of the ear, containing the cochlea, vestibule, and semicircular canals, crucial for hearing and balance.