Find the domain of `f(x) = (3^x)/(x+1)`

Answer

To find the domain of the function \( f(x) = \frac{3^x}{x+1} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the Function**: The function is given as \( f(x) = \frac{3^x}{x+1} \).

2. **Check the Denominator**: The denominator of the function is \( x + 1 \). A function is undefined when its denominator is zero, so we need to find when \( x + 1 = 0 \).

3. **Solve for \( x \)**:
\[ x + 1 = 0 \implies x = -1 \]
This means that the function is undefined at \( x = -1 \).

4. **Determine the Domain**: Since \( 3^x \) is defined for all real numbers, the only restriction on the domain comes from the denominator. Therefore, the domain of \( f(x) \) is all real numbers except \( -1 \).

5. **Express the Domain in Interval Notation**: The domain can be expressed as:
\[ \text{Domain} = (-\infty, -1) \cup (-1, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{3^x}{x+1} \) is \( (-\infty, -1) \cup (-1, \infty) \).