Questions: Find the domain of the function in interval notation: f(x) = 1/(x+2)

Find the domain of the function in interval notation: f(x) = 1/(x+2)
Transcript text: Find the domain of the function in interval notation: $f(x)=\frac{1}{x+2}$
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Solution

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Solution Steps

Step 1: Identify the function and its restrictions

The function given is \( f(x) = \frac{1}{x+2} \). For a rational function, the denominator cannot be zero because division by zero is undefined.

Step 2: Set the denominator not equal to zero

To find the domain, set the denominator \( x + 2 \) not equal to zero: \[ x + 2 \neq 0 \]

Step 3: Solve for \( x \)

Solve the inequality \( x + 2 \neq 0 \): \[ x \neq -2 \]

Step 4: Express the domain in interval notation

The domain of the function includes all real numbers except \( x = -2 \). In interval notation, this is written as: \[ (-\infty, -2) \cup (-2, \infty) \]

Final Answer

\(\boxed{(-\infty, -2) \cup (-2, \infty)}\)

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