Consider the function : f ( x ) = [ x ] + ∣1 − x ∣ , − 1 ≤ x ≤ 3 where [ x ] is the greatest integer function. Statement 1: f is not continuous at x = 0 , 1 , 2 and 3 Statement 2:f(x)= = − x , 1 − x ,

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Consider the function : f ( x ) = [ x ] + ∣1 − x ∣ , − 1 ≤ x ≤ 3 where [ x ] is the greatest integer function. Statement 1: f is not continuous at x = 0 , 1 , 2 and 3 Statement 2:f(x)= = − x , 1 − x , 1 + x , 2 + x , ​ − 1 ≤ x < 0 0 ≤ x < 1 1 ≤ x < 2 2 ≤ x ≤ 3 ​

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Let f ( x ) = [ x ] + ∣1 − x ∣ , − 1 ≤ x ≤ 3 where [ x ] = greatest integer function. f is not continuous at x = 0 , 1 , 2 , 3 But in statement-2 f ( x ) is continuous at x = 3 . Hence, statement-1 is true and 2 is false.

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