A) 5
B) 7
C) 9
D) 11
Correct Answer: B
Solution :
[b] Here \[1<x<3\] and in this interval \[{{x}^{2}}\] is an increasing functions, thus, \[1<{{x}^{2}}<9\] \[[{{x}^{2}}]=1,1\le x<\sqrt{2}=2,\sqrt{2}\le x<\sqrt{3}\] \[=3,\sqrt{3}\le x<2=4,2\le x<\sqrt{5}\] \[=5,\sqrt{5}\le x<\sqrt{6}=6,\sqrt{6}\le x<\sqrt{7}\] \[=7\sqrt{7}\le x<\sqrt{8}=8,\sqrt{8}\le x<3\] Clearly, \[[{{x}^{2}}]\] and also \[{{a}^{[{{x}^{2}}]}}\] is discontinuous and not differentiable at only 7 points, \[x=\sqrt{2},\sqrt{3},2,\sqrt{5},\sqrt{6}\sqrt{7},\sqrt{8}\]
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