The Surface Area of a Sphere Is $f ( x ) = 4 \pi x ^ { 2 }$

question 266

Multiple Choice

The surface area of a sphere is $f ( x ) = 4 \pi x ^ { 2 }$ square inches, where x is the radius of the sphere in inches. Find the inverse of this function.

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

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Definitions:

Ace of Hearts

A playing card in the deck of standard playing cards, distinguished by a single heart symbol and an ace rank.

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In a standard deck of playing cards, it refers to any jack, queen, or king, each of which has a picture of a face.

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In card games, an ace refers to a playing card that typically ranks the highest in its suit.

Lowest 4%

Refers to the bottom 4% of data points in a distribution, highlighting the far left end of the data spectrum or values significantly below the median.