AP EAMCET · Maths · Functions
The domain of the function \(f(x)=\sqrt{\log _{0.5} x !}\) is
- A \(\{0,1,2,3, \ldots\}\)
- B \(\{1,2,3, \ldots\}\)
- C \((0, \infty)\)
- D \(\{0,1\}\)
Answer & Solution
Correct Answer
(B) \(\{1,2,3, \ldots\}\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)=\sqrt{\log _{0.5} x !}\) So, \(f(x)\) will be defined when, \(\begin{aligned} & \log _{0.5} x ! \geq 0 \\ & x ! \leq(0.5)^0 \\ & x ! \leq 1 \quad \therefore x \in\{0,1\} \end{aligned}\) Hence, the domain of the function is \(\{0,1\}\).
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