JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \([ x ]\) denote the greatest integer function and \(f ( x )=\max \{1+ x +[ x ], 2+ x , x +2[ x ]\}, 0 \leq x \leq 2\). Let \(m\) be the number of points in \([0,2]\), where \(f\) is not continuous and \(n\) be the number of points in \((0,2)\), where \(f\) is not differentiable. Then \((m+n)^2+2\) is equal to:
- A \(11\)
- B \(2\)
- C \(6\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
Let \(g(x)=1+ x +[ x ]=\left\{\begin{array}{cc}1+ x ; & x \in[0,1) \\ 2+ x ; & x \in[1,2) \\ 5 ; & x =2\end{array}\right.\) \(\lambda(x)=x+2[x]=\left\{\begin{array}{cc}x ; & x \in[0,1) \\ x+2 ; & x \in[1,2) \\ 6 ; & x=2\end{array}\right.\) \(r(x)=2+x\)…
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