Solve the Problem $f ( x ) = e ^ { x - 1 } + 3$

question 436

Multiple Choice

Solve the problem.
-Given that $f ( x ) = e ^ { x - 1 } + 3$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$ .

• A) \(f ^ { - 1 } ( x ) = \ln ( x - 3 ) + 1\), domain \(= ( 3 , \infty )\), range \(= ( - \infty , \infty )\)
• B) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 1 ) + 3\), domain \(= ( 3 , \infty )\), range \(= ( - \infty , \infty )\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 3 ) + 1\), domain \(= ( 0 , \infty )\), range \(= ( 0 , \infty )\)
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 1 ) + 3\), domain \(= ( - \infty , \infty )\), range \(= ( - \infty , \infty )\)

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Definitions:

Linehaul Highway

A major transportation route designed for the efficient movement of goods and passengers over long distances.

Fully-Oscillating

Refers to a component or system, typically in heavy machinery, that has the ability to move or pivot freely in all directions.

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refers to surfaces or structures that are connected in a way that allows for movement or adjustment, often found in machinery or anatomical structures to enable flexibility and range of motion.

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