Find the Domain e^x-5+6e^(-x)

Problem

ex−5+6*e(−x)

Solution

1. Identify the components of the expression. The expression consists of three terms: ex −5 and 6*e(−x)

2. Analyze the exponential functions. The natural exponential function eu is defined for all real values of u

3. Check the exponents for restrictions. The first exponent is x which is defined for all real numbers. The second exponent is −x which is also defined for all real numbers.

4. Determine if there are any denominators or radicals. There are no denominators that could be zero and no even-indexed radicals that could have negative radicands.

5. Conclude the domain. Since there are no restrictions on x for any part of the expression, the domain is the set of all real numbers.

Final Answer

Domain:(−∞,∞)

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