Find the Domain

Problem

(√(3,m)−2√(3,n))*(√(3,m)+2√(3,n))

Solution

1. Identify the function type for each term in the expression. The expression consists of cube roots of variables m and n

2. Recall the domain rules for radical functions. For any root √(k,x) if k is an odd integer (like 3), the radicand x can be any real number.

3. Determine the constraints for m Since m is inside a cube root, there are no restrictions on its value.

4. Determine the constraints for n Since n is inside a cube root, there are no restrictions on its value.

5. Conclude that the domain consists of all real numbers for both variables.

Final Answer

Domain: *{[(m,n),m∈ℝ,n∈ℝ]}

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