Find Functions F and G So That F $f \circ g = H$

question 30

Multiple Choice

Find functions f and g so that f $f \circ g = H$
- $$H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$$

• A) \(f ( x ) = 5 - 2 x ^ { 3 } ; g ( x ) = x ^ { 2 }\)
• B) \(f ( x ) = x ^ { 2 } ; g ( x ) = 5 - 2 x ^ { 3 }\)
• C) \(f ( x ) = ( 5 - 2 x ) ^ { 3 } ; g ( x ) = x ^ { 2 }\)
• D) \(f ( x ) = x ^ { 3 } ; g ( x ) = ( 5 - 2 x ) ^ { 2 }\)

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Definitions:

Horizontal Supply Curve

Represents a market situation where the supply of a good is perfectly elastic, indicating the supplier is willing to sell any quantity at a fixed price.

Linear

A straight-line relation in mathematics that expresses a constant rate of increase or decrease between variables.

Deadweight Loss

A loss in economic efficiency that can occur when equilibrium for a good or a service is not achieved or is not achievable.

Inverse Demand Function

A mathematical function that describes how the quantity demanded of a good or service varies with its price, expressed as price as a function of quantity demanded.