Find the Domain ( cube root of 5^-1)/(60/(y^2))

Problem

√(3,5(−1))/60/(y2)

Solution

1. Identify the expression structure. The expression is a fraction where the denominator is 60/(y2)

2. Determine the constraints for the domain. In a rational expression, the denominator cannot be equal to zero.

3. Analyze the denominator 60/(y2) For this fraction to be defined, its own denominator y2 must not be zero.

y2≠0

y≠0

4. Analyze the entire expression. For the total fraction to be defined, the divisor 60/(y2) must not be zero.

60/(y2)≠0

5. Solve the second constraint. Since the numerator 60 is a constant and never zero, the fraction 60/(y2) can never be zero for any value of y where it is defined.

6. Check the numerator √(3,5(−1)) The cube root of a constant is defined for all real numbers, so it imposes no additional restrictions on y

7. Combine the restrictions. The only value that makes the expression undefined is y=0

Final Answer

Domain: *{[y∈ℝ,y≠0]}

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