For the Given Function, Find the Domain and Range of Both

question 149

Multiple Choice

For the given function, find the domain and range of both f(x) and ${ f } ^ { - 1 } ( \mathrm { x } ) .$
-{(6, -12) , (5, -11) , (3, -10) , (1, -9) }

• A) f: domain: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• \(~~~~\)range: \(\{ 6,5,3,1 \}\)
• \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ 6,5,3,1 \}\)
• \(~~~~\)range: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• B) f: domain: \(\{ 6,5,3,1 \}\)
• \(~~~~\)range: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• \(~~~~\)range: \(\{ 6,5,3,1 \}\)
• C) f: domain: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• \(~~~~\)range: \(\{ 6,5,3,1 \}\)
• \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• \(~~~~\)range: \(\{ 6,5,3,1 \}\)
• D) f: domain: \(\{ 6,5,3,1 \}\)
• \(~~~~\)range: \(\{ - 12 , - 11 , - 10 , - 9 \}\)
• \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ 6,5,3,1 \}\)
• \(~~~~\)range: \(\{ - 12 , - 11 , - 10 , - 9 \}\)

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Definitions:

Price-taker Industry

An industry in which individual firms have no control over the price of their product and must accept the market price set by the forces of supply and demand.

Price-taker Industry

An industry in which individual firms have no control over the price of their product; they "take" the market price as given.

Long-run Equilibrium

A state in which all factors of production and costs are variable, and firms no longer have any incentives to enter or exit the market, resulting in an optimal allocation of resources.