Find the Domain ( square root of 4-x^2)/(x-3)

Problem

√(,4−x2)/(x−3)

Solution

1. Identify the constraints for the square root function. The radicand must be greater than or equal to zero for the expression to be defined in the set of real numbers.

4−x2≥0

2. Solve the quadratic inequality for x

x2≤4

−2≤x≤2

3. Identify the constraints for the rational function. The denominator cannot be equal to zero.

x−3≠0

x≠3

4. Determine the intersection of the two conditions. Since the interval [−2,2] does not include the value 3 the restriction x≠3 is already satisfied by the first condition.

x∈[−2,2]

Final Answer

Domain:{[x∈ℝ,−2≤x≤2]}

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