Questions: Find the domain of the function. f(x)=(x-8)/(x+7) The domain of f(x)=(x-8)/(x+7) is . (Type your answer in interval notation.)

Transcript text: Find the domain of the function. \[ f(x)=\frac{x-8}{x+7} \] The domain of $f(x)=\frac{x-8}{x+7}$ is $\square$ . (Type your answer in interval notation.)

Solution

Solution Steps

To find the domain of the function $ f(x) = \frac{x-8}{x+7} $, we need to determine the values of $ x $ for which the function is defined. The function is undefined when the denominator is zero. Therefore, we need to find the value of $ x $ that makes $ x+7 = 0 $ and exclude it from the domain.

Step 1: Identify the Denominator

To find the domain of the function $ f(x) = \frac{x-8}{x+7} $, we first identify the denominator of the function, which is $ x + 7 $.

Step 2: Determine When the Denominator is Zero

The function is undefined when the denominator is zero. Therefore, we solve the equation: \[ x + 7 = 0 \] Solving for $ x $, we get: \[ x = -7 \]

Step 3: Define the Domain

The domain of the function $ f(x) $ includes all real numbers except $ x = -7 $. In interval notation, this is expressed as: \[ (-\infty, -7) \cup (-7, \infty) \]