Find the Domain 3e^x+8e^(-x)=10

Problem

3*e^x+8*e^(−x)=10

Solution

1. Identify the type of expression. The expression 3*e^x+8*e^(−x) is a sum of two exponential terms.

2. Analyze the components. The natural exponential function e^u is defined for all real numbers u

3. Check for restrictions. There are no denominators that could be zero, no square roots of negative numbers, and no logarithms of non-positive numbers in the expression.

4. Determine the domain. Since x and −x are defined for all real numbers, the entire expression is defined for all real values of x

Final Answer

Domain:(−∞,∞)

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