Find the Domain

Problem

√(3,5(3/2))/√(3,3(3/2))=x

Solution

1. Identify the nature of the expression. The expression is a constant value assigned to the variable x

2. Analyze the components for potential restrictions. The expression involves cube roots and constants in the denominator.

3. Check the denominator. The denominator is √(3,3(3/2)) which is a non-zero constant.

4. Check the radicals. Cube roots are defined for all real numbers, and the radicands 5(3/2) and 3(3/2) are positive real numbers.

5. Determine the domain. Since there are no variables in the expression on the left side and no values that result in division by zero or undefined roots, the equation is defined for all real numbers if x is considered a function of no variables, or simply that the expression itself is always defined. In the context of finding the domain of the equation x=constant x is a defined real number.

Final Answer

Domain: *(−∞,∞)

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