Find the domain of the following functions:
`(x-2)/(x+4)`

Answer

To find the domain of the function \( f(x) = \frac{x-2}{x+4} \), we need to determine the values of \( x \) for which the function is defined.

### Step 1: Identify the function
We start with the function:
\[ f(x) = \frac{x-2}{x+4} \]

### Step 2: Determine the denominator
The function is a rational function, which means it is defined as long as the denominator is not equal to zero. Therefore, we need to find when the denominator \( x + 4 \) is equal to zero.

### Step 3: Set the denominator to zero
Set the denominator equal to zero:
\[ x + 4 = 0 \]

### Step 4: Solve for \( x \)
Now, solve for \( x \):
\[ x = -4 \]

### Step 5: Exclude the value from the domain
Since the function is undefined when \( x = -4 \), we exclude this value from the domain. Thus, the domain of the function is all real numbers except \( -4 \).

### Step 6: Write the domain in interval notation
The domain can be expressed in interval notation as:
\[ \text{Domain} = (-\infty, -4) \cup (-4, \infty) \]

### Final Answer
The domain of the function \( f(x) = \frac{x-2}{x+4} \) is:
\[ \text{Domain} = \{ x \in \mathbb{R} \mid x \neq -4 \} \]

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