Question

find the domain of the function.

$h(x) = \dfrac{11}{\dfrac{6}{x} - 1}$

what is the domain of $h$?

\boxed{} (type your answer in interval notation.)

Explanation:

Step1: Identify undefined points

The function \( h(x)=\frac{11}{\frac{6}{x}-1} \) is undefined when the denominator is zero or when \( x = 0 \) (since \( \frac{6}{x} \) is undefined at \( x = 0 \)). First, find when the denominator \( \frac{6}{x}-1 = 0 \).
Solve \( \frac{6}{x}-1 = 0 \):
Add 1 to both sides: \( \frac{6}{x}=1 \)
Multiply both sides by \( x \) (assuming \( x
eq0 \)): \( 6 = x \)
So the denominator is zero when \( x = 6 \), and the function is also undefined at \( x = 0 \).

Step2: Determine the domain

The domain is all real numbers except \( x = 0 \) and \( x = 6 \). In interval notation, this is \( (-\infty, 0)\cup(0, 6)\cup(6, \infty) \).

Answer:

\( (-\infty, 0)\cup(0, 6)\cup(6, \infty) \)