Find the Domain x=8y^2

Problem

x=8*y2

Solution

1. Identify the type of equation. The equation x=8*y2 defines x as a function of y However, the standard convention for finding the domain is to determine the set of all possible input values (x for which the output (y is a real number.

2. Solve for y in terms of x to see the restrictions on x

y2=x/8

3. Apply the square root property to isolate y

y=±√(,x/8)

4. Determine the restriction for the square root. For y to be a real number, the expression inside the square root must be non-negative.

x/8≥0

5. Solve the inequality for x Multiplying both sides by 8 does not change the inequality sign.

x≥0

6. Express the domain in interval notation. Since x can be any value from 0 to infinity, including 0, the domain is [0,∞)

Final Answer

Domain:[0,∞)

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