Question:
The domain of the function
\[
f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}}
\]
\text{is:}
The domain of the function
\[
f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}}
\]
\text{is:}
Show Hint
For square root functions, ensure the expression inside the root is non-negative to determine the domain.
Updated On: Jan 12, 2026
- \( (-\infty, 2] \)
- \( (2, \infty) \)
- \( (-\infty, 2) \)
- \( [2, \infty) \)
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The Correct Option is A
Solution and Explanation
To find the domain, solve the inequality within the square root to ensure that the expression under the root is non-negative.
Final Answer: \[ \boxed{(-\infty, 2]} \]
Final Answer: \[ \boxed{(-\infty, 2]} \]
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