AP EAMCET · Maths · Continuity and Differentiability
If \(f: R \rightarrow R\) is defined by \(f(x)=x-[x]\), where \([x]\) is the greatest integer not exceeding \(x\), then the set of discontinuous of \(f\) is
- A the empty set
- B \(R\)
- C \(Z\)
- D \(N\)
Answer & Solution
Correct Answer
(C) \(Z\)
Step-by-step Solution
Detailed explanation
We know that, \[ f(x)=\left\{\begin{array}{cc} x-(n-1) & \text { for }-1 < x < n \\ 0 & \text { for } x=n \\ x-n & \text { for } n < x < n+1 \end{array}\right. \] where \(n \in z\) Now, we check the continuity at \(x=n\)…
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