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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)= = array cc -x, & -1 x < 0 1-x, & 0 x < 1 1+x, & 1 x < 2 2+x, & 2 x 3 array

Options

  1. AStatement 1 is true; Statement 2 is false,
  2. BStatement 1 is true; Statement 2 is true; Statement 2 is not correct explanation for Statement 1.
  3. CStatement 1 is true; Statement 2 is true; Statement It is a correct explanation for Statement 1.
  4. DStatement 1 is false; Statement 2 is true.

Correct answer

A. Statement 1 is true; Statement 2 is false,

Step-by-step solution

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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