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) \(f ^ { - 1 } ( x ) = 2 \sqrt { \pi x }\)

Evaluate economic performance and standard of living across countries.

Understand the influence of Leonardo's artistic techniques and preferences on contemporary artists.

Recognize the role of inexpensive drawing materials in promoting art during the Cinquecento.

Identify Michelangelo's prioritization of emotion in sculpture over traditional ideal beauty standards.

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Definitions:

Nuts

Hard-shelled seeds of certain plants that are generally edible and nutritious, often eaten raw, roasted, or used as ingredients in cooking.

Berries

Small, pulpy, and often edible fruits, typically juicy, rounded, brightly colored, and seed-containing, consumed worldwide in various forms.

Utility Function

A mathematical representation of how individual preferences or consumption bundles yield levels of satisfaction or utility.

Budget Constraint

A representation of all the combinations of goods and services a consumer can afford to buy given their income and the prices of the goods.