Question

find the domain of the function.
h(x) = \frac{7}{\frac{2}{x} - 1}
what is the domain of h?
\square (type your answer in interval notation.)

Explanation:

Step1: Identify denominator restrictions

First, the inner denominator $x$ cannot be 0, so $x
eq 0$.

Step2: Set outer denominator to non-zero

The overall denominator $\frac{2}{x} - 1$ cannot equal 0:

$$\frac{2}{x} - 1 eq 0$$

Step3: Solve the inequality

Rearrange and solve for $x$:

$$\frac{2}{x} eq 1 \implies 2 eq x$$

Step4: Combine restrictions

$x$ cannot be 0 or 2, so we split the real number line into intervals excluding these values.

Answer:

$(-\infty, 0) \cup (0, 2) \cup (2, \infty)$