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

question 121

Multiple Choice

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

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

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Definitions:

Time Is A Map

A metaphorical expression implying that time can be organized, navigated, and understood in a structured way, similar to how a map organizes and represents spatial data.

Flow Time

The duration of time a process takes from start to finish, often used to measure the efficiency of production or service systems.

Leisure Time

Free time not occupied by work or essential tasks, which can be used for rest, relaxation, or activities of personal interest.

Occasion Time

Specific moments or periods designated for particular events, activities, or celebrations, often marked by cultural, social, or personal significance.