Find the domain of the following functions:
`(1)/(x+1)`

Answer

To find the domain of the function \( f(x) = \frac{1}{x + 1} \), we follow these steps:

### Step 1: Identify the function
We have the function:
\[ f(x) = \frac{1}{x + 1} \]

### Step 2: Determine the condition for the function to be defined
For a rational function \( \frac{a}{b} \), the denominator \( b \) cannot be zero. Therefore, we need to find when the denominator \( x + 1 \) is not equal to zero.

### Step 3: Set the denominator not equal to zero
Set the denominator equal to zero and solve for \( x \):
\[ x + 1 \neq 0 \]
\[ x \neq -1 \]

### Step 4: State the domain
The domain of the function is all real numbers except the value that makes the denominator zero. Thus, we can express the domain in interval notation:
\[ \text{Domain} = (-\infty, -1) \cup (-1, \infty) \]

### Final Answer
The domain of the function \( f(x) = \frac{1}{x + 1} \) is all real numbers except \( -1 \).

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