Pregunta
Decide whether the following statement is true or false.
The domain of the exponential function
, is the set of all real numbers.
Choose the correct answer below.
False
True
The domain of the exponential function
Choose the correct answer below.
False
True
Ask by Jimenez Lewis. in the United States
Mar 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The statement is True.
Solución
-
The exponential function is given by
where and . -
Since the base
is positive and not equal to 1, the function is defined for every real number . -
Therefore, the domain of
is the set of all real numbers.
Thus, the statement is True.
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Como
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Bonus Knowledge
True! The domain of the exponential function
where
and
is indeed the set of all real numbers. This means that you can plug any real number into the function and get a valid output, making it quite versatile in mathematical applications.
Exponential functions are utilized in a plethora of real-world scenarios, from modeling population growth and radioactive decay to analyzing interest rates in finance. Their unique ability to grow swiftly or decay rapidly makes them invaluable across scientific fields and economics.

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