Find the Domain square root of 36-4x^2

Problem

√(,36−4*x2)

Solution

1. Identify the condition for the domain of a square root function, which requires the radicand (the expression inside the square root) to be greater than or equal to zero.

36−4*x2≥0

2. Isolate the term containing the variable by subtracting 36 from both sides of the inequality.

−4*x2≥−36

3. Divide both sides by −4 remembering to flip the inequality sign because of the division by a negative number.

x2≤9

4. Solve the quadratic inequality by taking the square root of both sides, which defines the interval for x

|x|≤3

5. Express the solution in interval notation to represent all possible values of x

−3≤x≤3

Final Answer

Domain:[−3,3]

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