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Discuss the continuity of the functionf(x) = |x -1|"at" x=1

Answer»

Solution :By definition f(x) `{:{(x-1,XGE 1), (-(x-1), x lt1):}`
CLEARLY, the function is DEFINED at 1 and f(1)=0
LEFT hand limit of at 1 is
`underset(x to 1^(-))limf(x) = underset(x to1) LIM (-x+1)=0`
Similarly the right hand limit of f at 1. is
`underset(x to 1^(+))limf(x) = underset(x to 1^(+))lim ( x-1)=0 `
Thus, the left hand limit, right hand limit and the value of the function coincide at x =1 . Hence the function is continuous at x =1 .


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