Question

state the domain of the function. f(x)=\frac{1}{x - 6} the domain of the function f(x) is \boxed{...} (type your answer in interval notation.)

Explanation:

Step1: Identify undefined point

For the function \( f(x)=\frac{1}{x - 6} \), the denominator cannot be zero. So, solve \( x - 6=0 \), which gives \( x = 6 \).

Step2: Determine domain intervals

The function is defined for all real numbers except \( x = 6 \). In interval notation, this is \( (-\infty, 6)\cup(6, \infty) \).

Answer:

\((-\infty, 6)\cup(6, \infty)\)