Here are the essential concepts you must grasp in order to answer the question correctly.
Functions and Graphs
A function is a relation that assigns exactly one output for each input. In this problem, we have two functions: y = x - √(x - 2) and y = 4. Understanding how to graph these functions helps visualize their intersection points, which represent the solutions to the equation.
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Solving Equations
To find the values of x that satisfy the given conditions, we need to set the two equations equal to each other: x - √(x - 2) = 4. This involves isolating the variable and may require algebraic manipulation, such as squaring both sides to eliminate the square root.
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Domain of Functions
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function y = x - √(x - 2), the expression under the square root must be non-negative, leading to the condition x - 2 ≥ 0, or x ≥ 2. Understanding the domain is crucial for identifying valid solutions.
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