Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Equations
A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. In the context of the given question, the equation x = y² - 1 can be rearranged to form a standard quadratic equation in terms of y, allowing for the application of methods such as factoring or the quadratic formula to find the values of y.
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Square Roots
Square roots are the values that, when multiplied by themselves, yield the original number. In solving the equation x = y² - 1, isolating y² leads to y = √(x + 1). Understanding how to manipulate square roots is essential, especially since the problem specifies y ≥ 0, indicating that only the non-negative root is relevant.
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Domain and Range
The domain refers to the set of all possible input values (x-values) for a function, while the range refers to the set of possible output values (y-values). In this problem, the condition y ≥ 0 restricts the range of the solution, which is crucial for determining valid solutions to the equation and understanding the behavior of the function represented by the equation.
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