Find the Domain xx=yyy

Problem

x=y3

Solution

1. Identify the independent and dependent variables. In the equation x=y3 x is expressed as a function of y However, the domain of a relation or function typically refers to the set of all possible input values for x

2. Solve for y in terms of x to treat x as the input. To isolate y take the cube root of both sides.

y=√(3,x)

3. Analyze the restrictions on the input x The cube root function √(3,x) is defined for all real numbers because any real number (positive, negative, or zero) has exactly one real cube root.

4. Determine the interval. Since there are no values of x that result in an undefined expression or a non-real number, the domain is all real numbers.

Final Answer

Domain:(−∞,∞)

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