Calculate $g ( x )$ , Where $g = f ^ { - 1 }$

question 9

Multiple Choice

Calculate $g ( x )$ , where $g = f ^ { - 1 }$ . State the domain and range of $g$ . Calculate $g ^ { \prime } ( a )$
$$f ( x ) = \frac { 1 } { x - 3 } , x > 3 ; a = 2$$

• A)\(g ( x ) = 3 + \frac { 1 } { x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 4 }\), domain \(= ( 0 , \infty )\), range \(= ( 3 , \infty )\)
• B)\(g ( x ) = 4 + \frac { 1 } { x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 4 }\), domain \(= ( 0 , \infty )\), range \(= ( 4 , \infty )\)
• C)\(g ( x ) = 2 + \frac { 1 } { x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 2 }\), domain \(= ( 0 , \infty )\), range \(= ( 3 , \infty )\)
• D)\(g ( x ) = 4 + \frac { 1 } { 2 x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 8 }\), domain \(= ( 0 , \infty )\), range \(= ( 3 , \infty )\)
• E)\(g ( x ) = 1 + \frac { 3 } { x } , g ^ { \prime } ( 2 ) = - \frac { 3 } { 4 }\), domain \(= ( 0 , \infty )\), range \(= ( 1 , \infty )\)

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Definitions:

Containment Doctrine

A foreign policy strategy aimed at preventing the expansion of a hostile power or ideology, particularly associated with the United States' approach to the Soviet Union during the Cold War.

Cold War

A period of geopolitical tension between the Soviet Union and the United States and their respective allies from the end of World War II in 1945 until the dissolution of the Soviet Union in 1991, characterized by threats, propaganda, and other measures short of open warfare.

Red Scare

Periods of intense fear and suspicion in the United States regarding the influence of communism and anarchists, notably after World War I and during the Cold War.