Questions: Find the domain of the function. f(x) = 7 / (x - 14)

Solution Steps

To find the domain of the function \( f(x) = \frac{7}{x-14} \), 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 values of \( x \) that do not make the denominator zero.

We are given the function \( f(x) = \frac{7}{x-14} \). To find the domain, we need to determine the values of \( x \) for which this function is defined.

The function is undefined when the denominator is equal to zero. Therefore, we set the denominator \( x - 14 \) equal to zero and solve for \( x \): \[ x - 14 = 0 \implies x = 14 \]

The domain of the function consists of all real numbers except the value that makes the denominator zero. Thus, the domain can be expressed as: \[ \text{Domain} = \mathbb{R} \setminus \{14\} \] This means that the function is defined for all real numbers except \( x = 14 \).

Final Answer