Find the Domain x^2-2y-1=0

Problem

x2−2*y−1=0

Solution

1. Identify the type of equation. This is a quadratic equation in terms of x and a linear equation in terms of y representing a parabola.

2. Solve for y to express the relation as a function of x

2*y=x2−1

y=(x2−1)/2

3. Analyze the resulting function ƒ(x)=1/2*x2−1/2 This is a polynomial function.

4. Determine the constraints on the input x Since there are no square roots of negative numbers, no denominators that could be zero, and no logarithms, the function is defined for all real numbers.

5. State the domain in interval notation.

Final Answer

Domain:(−∞,∞)

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