The number of points of discontinuity of the function f (x) = [ 2 x 2 ] - [$\sqrtx$], x$\ in $[0, 4] , where [$\cdot$] denotes the greatest integer function is ________
Step-by-Step Solution
Key Concept: Break the function at its$formula-changing$points and compare$one-sided$limits or derivatives there.
Check for [ 2 x 2 ] and [$\sqrtx$] becomes integers. (8) {0, 1,$\sqrt{2}$, 2,$\sqrt{6}$,$\sqrt{8}$,$\sqrt{10}$,$\sqrt{12}$,$\sqrt{14}$, 4} 2 Continuous at 0 , continuous at 4 + - [ x 2 ] = [$\sqrtx$] , occurs at x =$\sqrt{2}$$\Rightarrow$ Not continuous
Correct Answer: 8