Domain
The domain of a function is the set of all possible input values for the function
The domain of a function is the set of all possible input values for the function. In other words, it is the set of values for which the function is defined.
To illustrate this concept, let’s consider a specific example. Suppose we have a function f(x) = √(4 – x^2).
In this case, the function represents a semi-circle centered at (0,0) with a radius of 2. Since the square root of a negative number is undefined in the real number system, the expression inside the square root cannot be negative. Therefore, 4 – x^2 must be greater than or equal to 0.
To find the domain, we set 4 – x^2 ≥ 0 and solve for x.
Starting with the inequality, we add x^2 to both sides: 4 ≥ x^2.
Taking the square root of both sides, we have |x| ≤ 2.
Therefore, the domain of the function is the set of all x such that -2 ≤ x ≤ 2.
In interval notation, the domain can be written as [-2, 2].
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