Find the Domain (e^(3x))/(3*e^(4x))

Problem

(e(3*x))/(3*e(4*x))

Solution

1. Identify the type of function. The expression is a rational function involving exponential terms.

2. Determine the conditions for the domain. For a rational expression, the denominator must not be equal to zero.

3. Set up the inequality for the denominator: 3*e(4*x)≠0

4. Solve for x Since the exponential function eu is always strictly greater than zero for all real numbers u the product 3*e(4*x) is always positive and never zero.

5. Conclude that there are no values of x that make the denominator zero, meaning the function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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