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

question 61

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

---

Definitions:

Administrative Assistant

A person who provides support and assists in the efficient operation of an office or organization through various tasks and coordination.

Home Furnishings

Refers to movable items placed within a living space to make it suitable and comfortable for living or working.

Global Shipping

The process of transporting goods across the world via sea, air, or land routes.

Reasonable Review

The process of examining or assessing something carefully, with the expectation that the review is conducted fairly and judiciously.