Find the Domain y = log of x+2

Problem

y=(log_)(x+2)

Solution

1. Identify the restriction for the logarithmic function. The argument of a logarithm must be strictly greater than zero.

2. Set up the inequality based on the argument of the function.

x+2>0

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

x>−2

4. Express the domain in interval notation. Since x must be greater than −2 the interval starts at −2 (not included) and goes to infinity.

(−2,∞)

Final Answer

Domain:(−2,∞)

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