Question

find the domain of the function.
h(x)=\frac{7}{\frac{6}{x}-1}
what is the domain of h?
(type your answer in interval notation.)

Explanation:

Step1: Identify values that make denominator zero

The denominator of the function $h(x)=\frac{7}{\frac{6}{x}-1}$ cannot be zero. First, set $\frac{6}{x}-1 = 0$.
Solve $\frac{6}{x}-1=0$ for $x$. Add 1 to both sides: $\frac{6}{x}=1$. Then cross - multiply to get $x = 6$. Also, $x$ cannot be 0 because $\frac{6}{x}$ is undefined when $x = 0$.

Step2: Write domain in interval notation

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

Answer:

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