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

Problem

√(,x+3)/(x−4)

Solution

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

x+3≥0

2. Solve the inequality for x by subtracting 3 from both sides.

x≥−3

3. Identify the restriction for the rational expression. The denominator cannot be equal to zero.

x−4≠0

4. Solve for the excluded value of x by adding 4 to both sides.

x≠4

5. Combine the restrictions to determine the domain. The value of x must be greater than or equal to −3 but cannot be equal to 4

[−3,4)∪(4,∞)

Final Answer

Domain:[−3,4)∪(4,∞)

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