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JEE Main 201325 AprilOnline
Exam
JEE Main
Year
2013
Date
25 April
Mode
Online
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2013 · 25 April · Online · Mathematics · Continuity and Differentiability

Consider the function : f(x)=[x]+|1-x|,-1 ≤ x ≤ 3 where [x] is the...

Consider the function : f(x)=[x]+∣1−x∣,−1≤x≤3f(x)=[x]+|1-x|,-1 \leq x \leq 3 where [x][x] is the greatest integer function. Statement 1: ff is not continuous at x=0,1,2x=0,1,2 and 3 Statement 2:f(x)= ==−x,−1≤x<01−x,0≤x<11+x,1≤x<22+x,2≤x≤3\begin{array}{cc}-x, & -1 \leq x < 0 \\ 1-x, & 0 \leq x < 1 \\ 1+x, & 1 \leq x < 2 \\ 2+x, & 2 \leq x \leq 3\end{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≤3f(x)=[x]+|1-x|,-1 \leq x \leq 3 where [x]=[x]= greatest integer function. ff is not continuous at x=0,1,2,3x=0,1,2,3 But in statement-2 f(x)f(x) is continuous at x=3x=3. Hence, statement-1 is true and 2 is false.
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