$\text { Find } f ^ {t } ( x ) \text { if } f ( x ) = \log _ { 5 } \left( \frac { x ^ { 3 } - 1 } { x ^ { 3 } - 6 } \right)$

question 150

Multiple Choice

$\text { Find } f ^ {t } ( x ) \text { if } f ( x ) = \log _ { 5 } \left( \frac { x ^ { 3 } - 1 } { x ^ { 3 } - 6 } \right)$

• A)\(f ^ { t } ( x ) = \frac { x ^ { 2 } - 5 } { \left( x ^ { 3 } - 1 \right) \left( x ^ { 2 } - 6 \right) }\)
• B) \(f ^ { t } ( x ) = \frac { \left( x ^ { 3 } - 1 \right) } { \left( x ^ { 3 } - 6 \right) \ln ( 5 ) }\)
• C)\(f ^ { t } ( x ) = \frac { - 15 x ^ { 2 } } { \left( x ^ { 3 } - 1 \right) \left( x ^ { 3 } - 6 \right) }\)
• D)\(f ^ { t } ( x ) = \frac { x ^ { 3 } - 6 } { \left( x ^ { 3 } - 1 \right) \ln ( 5 ) }\)
• E)\(f ^ { t } ( x ) = \frac { - 15 x ^ { 2 } } { \left( x ^ { 3 } - 1 \right) \left( x ^ { 3 } - 6 \right) \ln ( 5 ) }\)

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Definitions:

Increasing-cost Industry

An increasing-cost industry is one in which the entry of new firms raises the average costs of production, often due to limited resources or increasing prices for inputs.

Consumer Demand

The willingness and ability of consumers to purchase goods and services at different prices, influencing market dynamics and prices.

Market Price

The price of a good or service determined by supply and demand in a competitive market.

Purely Competitive Market

A market structure characterized by many buyers and sellers, homogeneous products, and no barriers to entry or exit, leading to minimal market power for individual firms.