Find the Domain 7 fourth root of 567y^4

Problem

7√(4,567*y4)

Solution

1. Identify the type of function. The expression is a radical with an even index (the fourth root).

2. Recall the rule for even roots. For any expression √(n,ƒ(y)) where n is even, the radicand ƒ(y) must be greater than or equal to zero to produce a real number.

3. Set up the inequality for the radicand.

567*y4≥0

4. Solve the inequality. Since 567 is a positive constant and y4 is always non-negative for any real number y (because any real number raised to an even power is ≥0, the product 567*y4 is always ≥0

5. Determine the domain. Since the inequality holds true for all real values of y the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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