Question Find the domain of the function $$ g(x)=\sqrt{\frac{-6}{x-1}} $$

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and express it in interval notation.

To find the domain of the function $$ g(x)=\sqrt{\frac{-6}{x-1}} $$, we need to consider the conditions under which the function is defined. The function involves a square root and a fraction, so we need to ensure that:

1. The expression inside the square root is non-negative.
2. The denominator of the fraction is not zero.

Let's analyze these conditions:

1. The expression inside the square root is $$\frac{-6}{x-1}$$. For the square root to be defined, this expression must be non-negative. However, since the numerator is negative (-6) and the denominator is $$x-1$$, the expression will always be negative. Therefore, there is no value of $$x$$ for which the expression inside the square root is non-negative.

2. The denominator of the fraction is $$x-1$$. The function is undefined when the denominator is zero, so we need to exclude $$x=1$$ from the domain.

Based on these conditions, the domain of the function is all real numbers except $$x=1$$. In interval notation, the domain is expressed as:

$$
\boxed{(-\infty, 1) \cup (1, \infty)}
$$
The domain of the function is $$(-∞, 1) \cup (1, ∞)$$.

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Find the domain of the function

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