KCET · Maths · Continuity and Differentiability
The function \(f(x)=[x]\), where \([x]\) denotes the greatest integer not greater than \(x\), is
- A continuous for all non-integral values of \(x\)
- B continuous only at positive integral values of \(\mathrm{x}\)
- C continuous for all real values of \(x\)
- D continuous only at rational values of \(x\)
Answer & Solution
Correct Answer
(A) continuous for all non-integral values of \(x\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=[x]\) from the graph we observe that \(f(x)=[x]\) discontinuous at every integral value of \(x\). That means, \(f(x)=[x]\). Continuous only for all non-integral values of \(\mathrm{x}\).
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