TS EAMCET · Maths · Functions
The set of all values of \(x\) and the set of all values of \(a\) for which the real valued function \(f(x)=\sqrt{\log _a(x-[x])}\) is defined are respectively
- A \(R-Z\) and \((0,1)\)
- B \(Z\) and \(R-\{0,1\}\)
- C \(Z\) and \((1, \infty)\)
- D \(R\) and \(R\)
Answer & Solution
Correct Answer
(A) \(R-Z\) and \((0,1)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sqrt{\log _a\{x-[x]\}}\) is defined It will be defined if \(\log _a\{x-[x]\} \geq 0\), so \(x-\{x\} \geq 1\) (Not possible) \(x-[x]>0\), so \(x \neq Z\) So, \(R-(Z)\) and \((0,1)\).
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