Questions: State the domain of the function. f(x)=4/(x-7) The domain of the function f(x) is (Type your answer in interval notation.)

Solution Steps

To determine the domain of the function \( f(x) = \frac{4}{x-7} \), we need to identify 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 the denominator zero and exclude it from the domain.

The function given is \( f(x) = \frac{4}{x-7} \). To determine the domain, we need to identify the values of \( x \) that make the denominator zero.

Set the denominator equal to zero and solve for \( x \): \[ x - 7 = 0 \implies x = 7 \] The function is undefined when \( x = 7 \).

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

Final Answer