Given That $f ( x ) = 5 \ln 2 x$

question 48

Multiple Choice

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

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