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Discuss the continuity of the function ` f(x) =|x|+|x-1|` in the interval [ -1,2]

Answer» Correct Answer - continuous
The given function may be expressed as
` f(x)={{:(( 1-2x)",","when" , 1-le x lt 0),(1",","when",0le x le 1),((2x-1)",","when",1 lt x le2):}`
Since a polynomial function as weill as a constant , if follows that f(x) is continuous when ` -1 x lt x lt 0, 0 lt x lt 0: 0 lt x lt 1 and 1 lt x lt 2 `
So , test the continuity at -1 , 0, 1 and 2
At x = -1 ` lim_( xto (-1) +) . f(x) = f( -1) ` so it is continuous at x =-1


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