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 \(= ( 1 , \infty )\)

---

Definitions:

Fixed Cost

Expenses that do not change with the level of production or output within a certain range or period.

Variable Cost

Costs that vary directly with the level of production or output, such as materials and labor.

Operating

The day-to-day activities or functions necessary for a business or organization to run effectively and efficiently.

Competitive Market

A market structure characterized by many buyers and sellers, free entry and exit, and a product for which there are many substitutes.