Solve the Problem $f ( x ) = 5 \ln 2 x$

question 389

Multiple Choice

Solve the problem.
-Given that $f ( x ) = 5 \ln 2 x$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } - 5 }\), domain \(= ( 0 , \infty )\), range \(= ( - \infty , \infty )\)
• B) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } / 5 }\), domain \(= ( - \infty , \infty )\), range \(= ( 0 , \infty )\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } - 5 }\), domain \(= ( - \infty , \infty )\), range \(= ( 0 , \infty )\)
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 2 } \mathrm { e } ^ { \mathrm { x } / 5 }\), domain \(= ( 0 , \infty )\), range \(= ( - \infty , \infty )\)

---

Definitions:

Entity

Something that exists as a particular and discrete unit, often referred to in philosophy, law, and technology.

Internal

Existing or situated within the confines of an object, individual, or group, often referring to inner qualities or operations.

External

Originating from or existing outside oneself or the subject being considered, often influencing it from the outside.

Stable Internal

Characteristics or attributes within a person that are enduring and consistent across different situations, influencing behavior and attitudes.