Find the Domain y^2-6y-10x-56=0

Problem

y2−6*y−10*x−56=0

Solution

1. Identify the type of equation. This is a quadratic equation in terms of y and a linear equation in terms of x which represents a parabola opening horizontally.

2. Isolate the term containing x to express x as a function of y

10*x=y2−6*y−56

3. Solve for x by dividing both sides by 10

x=(y2−6*y−56)/10

4. Determine the domain. In the context of a function x=ƒ(y) the domain refers to the possible values of the independent variable y Since the expression for x is a polynomial in y there are no restrictions such as division by zero or square roots of negative numbers.

5. Conclude that y can be any real number. In interval notation, this is (−∞,∞)

Final Answer

Domain:(−∞,∞)

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