Find the Domain f(x)=3x+2e^x

Problem

ƒ(x)=3*x+2*ex

Solution

1. Identify the components of the function ƒ(x) The function is a sum of a linear term 3*x and an exponential term 2*ex

2. Analyze the domain of the linear term 3*x A linear function is a polynomial, and polynomials are defined for all real numbers.

3. Analyze the domain of the exponential term 2*ex The natural exponential function ex is defined for all real numbers.

4. Determine the intersection of the domains. Since both 3*x and 2*ex are defined for all real numbers, their sum is also defined for all real numbers.

Final Answer

Domain:(−∞,∞)

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