Questions: Determine the domain of the function: 2. (g(x)=frac2x+1) Description: Domain Range Vertical Asymptote Horizontal Asymptote

$Determine the domain of the function: 2. (g(x)=frac2x+1) Description: Domain Range Vertical Asymptote Horizontal Asymptote$

Transcript text: Determine the domain of the function: 2. $g(x)=\frac{2}{x+1}$ Description: \begin{tabular}{|l|l|} \hline Domain & \\ \hline Range & \\ \hline Vertical Asymptote & \\ \hline Horizontal Asymptote & \\ \hline \end{tabular}

Solution

Solution Steps

To determine the domain of the function $ g(x) = \frac{2}{x+1} $, we need to identify the values of $ x $ for which the function is defined. The function is undefined when the denominator is zero.

Solution Approach

Identify the values of $ x $ that make the denominator zero.
Exclude these values from the domain.

Step 1: Identify the Function

The function given is $ g(x) = \frac{2}{x+1} $.

Step 2: Determine Where the Function is Undefined

To find the domain, we need to determine where the function is undefined. The function is undefined when the denominator is equal to zero: \[ x + 1 = 0 \] Solving for $ x $ gives: \[ x = -1 \]

Step 3: State the Domain

The domain of the function includes all real numbers except the value that makes the denominator zero. Therefore, the domain is: \[ \text{Domain} = \mathbb{R} \setminus \{-1\} \] This can be expressed as: \[ \text{Domain} = (-\infty, -1) \cup (-1, \infty) \]