Question
Download Solution PDFFind the domain of function \(f\left( x \right) = \;\frac{{2.3}}{{\sqrt {x - \left[ x \right]} }}\;\), where [.] represents the greatest integer function.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The real function f: R → R defined by f (x) = [x], x ∈R picks the value of the greatest integer less than or equal to x, is called the greatest integer function.
Thus f (x) = [x] = – 1 for – 1 ≤ x < 0
And f (x) = [x] = 0 for 0 ≤ x < 1
[x] = 1 for 1 ≤ x < 2
[x] = 2 for 2 ≤ x < 3 and so on
CALCULATIONS:
Given function is \(f\left( x \right) = \;\frac{{2.3}}{{\sqrt {x - \left[ x \right]} }}\;\)
As we know that \(0 \leqslant x - \left[ x \right] < 1,x \in R\)
For x ∈ Z, x – [x] = 0
So, domain is R – ZLast updated on Jul 8, 2025
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