The domain of the function
\(f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))\)
where [t] is the greatest integer function, is
\(f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))\)
where [t] is the greatest integer function, is
- \((-\sqrt\frac{5}{2},\frac{5-√5}{2})\)
- \((\frac{5-√5}{2},\frac{5+√5}{2})\)
- \((1,\frac{5-√5}{2})\)
- \((1,\frac{5+√5}{2})\)
The Correct Option is C
Solution and Explanation
The correct answer is(C): \((1,\frac{5-√5}{2})\)
![The domain of the function \(f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))\) where [t] is the greatest integer function, is](https://images.collegedunia.com/public/qa/images/content/2024_01_31/image_e6c230b61706702850578.png)
Taking intersection
\(x ∈(1,\frac{5-√5}{2})\)
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Concepts Used:
Range
The range in statistics for a provided data set is the difference between the highest and lowest values. For instance, if the provided data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, the range could also be described as the difference between the highest observation and lowest observation. The acquired result is called the range of observation. The range in statistics states the spread of observations.
